메뉴 건너뛰기




Volumn 231, Issue 2, 2000, Pages 217-251

Frontier between decidability and undecidability: A survey

Author keywords

Decidability versus undecidability; Discrete computations; Halting problem; Universality

Indexed keywords


EID: 0038387709     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(99)00102-4     Document Type: Article
Times cited : (57)

References (126)
  • 1
    • 0348170722 scopus 로고
    • Investigations on algorithmic questions of algebra
    • S.I. Adian, G.S. Makanin, Investigations on algorithmic questions of algebra, Proc. Steklov Inst. Math. (3) (1986) 207-226 (English translation, original in Trudy Matematicheskogo Instituta imeni Steklova 168 (1984)).
    • (1986) Proc. Steklov Inst. Math. , Issue.3 , pp. 207-226
    • Adian, S.I.1    Makanin, G.S.2
  • 2
    • 0346279940 scopus 로고
    • S.I. Adian, G.S. Makanin, Investigations on algorithmic questions of algebra, Proc. Steklov Inst. Math. (3) (1986) 207-226 (English translation, original in Trudy Matematicheskogo Instituta imeni Steklova 168 (1984)).
    • (1984) Trudy Matematicheskogo Instituta Imeni Steklova , vol.168
  • 3
    • 0028114541 scopus 로고
    • Molecular computation of solutions to combinatorial problems
    • L. Adleman, Molecular computation of solutions to combinatorial problems, Science 266 (1994) 1021-1024.
    • (1994) Science , vol.266 , pp. 1021-1024
    • Adleman, L.1
  • 8
    • 0026116803 scopus 로고
    • Undecidable problem about rational sets and contour words of polyominoes
    • D. Beauquier, Undecidable problem about rational sets and contour words of polyominoes, Inform. Proces. Lett. 37 (5) (1991) 257-263.
    • (1991) Inform. Proces. Lett. , vol.37 , Issue.5 , pp. 257-263
    • Beauquier, D.1
  • 9
    • 85010933273 scopus 로고
    • A decidability result about convex polyominoes
    • Imre Simon (Ed.), Proc. Latin American Symp. on Theoretical Informatics (LATIN '92)
    • D. Beauquier, M. Latteux, K. Slowinski, A decidability result about convex polyominoes, in: Imre Simon (Ed.), Proc. Latin American Symp. on Theoretical Informatics (LATIN '92), Lecture Notes in Computer Science, vol. 583, 1992, pp. 32-45.
    • (1992) Lecture Notes in Computer Science , vol.583 , pp. 32-45
    • Beauquier, D.1    Latteux, M.2    Slowinski, K.3
  • 10
    • 0015680909 scopus 로고
    • Logical reversibility of computation
    • C.H. Bennett, Logical reversibility of computation, IBM J. Res. Dev. 6 (1973) 525-532.
    • (1973) IBM J. Res. Dev. , vol.6 , pp. 525-532
    • Bennett, C.H.1
  • 11
    • 0003359740 scopus 로고
    • The undecidability of the domino problem
    • R. Berger, The undecidability of the domino problem, Mem. Amer. Soc. 66 (1966).
    • (1966) Mem. Amer. Soc. , vol.66
    • Berger, R.1
  • 13
    • 45249125746 scopus 로고
    • Self-reproduction in small cellular automata
    • J. Byl, Self-reproduction in small cellular automata, Physica D 34 (1989) 295-299.
    • (1989) Physica D , vol.34 , pp. 295-299
    • Byl, J.1
  • 14
    • 0030586641 scopus 로고    scopus 로고
    • The dynamics of discrete-time computation with application to recurrent neural networks and finite state machine extraction
    • M. Casey, The dynamics of discrete-time computation with application to recurrent neural networks and finite state machine extraction, Neural Comput. 8 (6) (1996) 1135-1178.
    • (1996) Neural Comput. , vol.8 , Issue.6 , pp. 1135-1178
    • Casey, M.1
  • 15
    • 0348170719 scopus 로고
    • Rule space transformations and one-dimensional cellular automata
    • J. Dassow, G. Rozenberg, A. Salomaa (Eds.), World Scientific, Singapore
    • G. Cattaneo, E. Formenti, G. Mauri, Rule space transformations and one-dimensional cellular automata, in: J. Dassow, G. Rozenberg, A. Salomaa (Eds.), Proc. 2nd Internat. Conf. Developments in Language Theory, World Scientific, Singapore, 1995, pp. 409-419.
    • (1995) Proc. 2nd Internat. Conf. Developments in Language Theory , pp. 409-419
    • Cattaneo, G.1    Formenti, E.2    Mauri, G.3
  • 16
    • 0347964474 scopus 로고
    • Some remarks on PCP(k) and related problems
    • V. Claus, Some remarks on PCP(k) and related problems, Bull. EATCS 12 (1980) 54-61.
    • (1980) Bull. EATCS , vol.12 , pp. 54-61
    • Claus, V.1
  • 18
    • 0001845146 scopus 로고
    • Unpredictable iterations
    • Colorado, University of Colorado
    • J.H. Conway, Unpredictable iterations, in Proc. 1972 Number Theory Conf. Boulder, Colorado, University of Colorado, 1972, pp. 49-52.
    • (1972) Proc. 1972 Number Theory Conf. Boulder , pp. 49-52
    • Conway, J.H.1
  • 19
    • 21144465453 scopus 로고
    • Computability properties of low-dimensional dynamical systems
    • Proc. 10th Symp. on Theoretical Aspects of Computer Science
    • M. Cosnard, M. Garzon, P. Koiran, Computability properties of low-dimensional dynamical systems, Proc. 10th Symp. on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, vol. 665, 1993, pp. 365-373.
    • (1993) Lecture Notes in Computer Science , vol.665 , pp. 365-373
    • Cosnard, M.1    Garzon, M.2    Koiran, P.3
  • 20
    • 0039067657 scopus 로고    scopus 로고
    • An aperiodic set of 13 Wang tiles
    • K. Culik II, An aperiodic set of 13 Wang tiles, Discrete Appl. Math. 160 (1996) 245-251.
    • (1996) Discrete Appl. Math. , vol.160 , pp. 245-251
    • Culik K. II1
  • 21
    • 0347541029 scopus 로고
    • Splicing semigroups of dominoes and DNA
    • K. Culik II, T. Harju, Splicing semigroups of dominoes and DNA, Discrete Appl. Math. 31 (1991) 261-277.
    • (1991) Discrete Appl. Math. , vol.31 , pp. 261-277
    • Culik K. II1    Harju, T.2
  • 22
    • 0347636215 scopus 로고
    • Small deterministic turing machines
    • Department of Mathematics, Karl Marx University of Economics, Budapest, 1988-4
    • V. Diekert, M. Kudlek, Small deterministic turing machines, Papers on Automata and Languages, Department of Mathematics, Karl Marx University of Economics, Budapest, 1988-4, 1989, pp. 77-87.
    • (1989) Papers on Automata and Languages , pp. 77-87
    • Diekert, V.1    Kudlek, M.2
  • 23
    • 0006491330 scopus 로고
    • Positive theory of a free semi-group
    • V.G. Durnev, Positive theory of a free semi-group, Dokl. Akad. Nauk SSSR 211 (1973) 772-774 (English transl. in Soviet Math. Dokl. 14 (1973)).
    • (1973) Dokl. Akad. Nauk SSSR , vol.211 , pp. 772-774
    • Durnev, V.G.1
  • 24
    • 0348170720 scopus 로고
    • V.G. Durnev, Positive theory of a free semi-group, Dokl. Akad. Nauk SSSR 211 (1973) 772-774 (English transl. in Soviet Math. Dokl. 14 (1973)).
    • (1973) Soviet Math. Dokl. , vol.14
  • 25
    • 0001208326 scopus 로고
    • The (generalized) Post correspondence problem with lists consisting of two words is decidable
    • A. Ehrnfeucht, J. Kerhumäki, G. Rozenberg, The (generalized) Post correspondence problem with lists consisting of two words is decidable, Theoret. Comput. Sci. 21 (1982) 119-144.
    • (1982) Theoret. Comput. Sci. , vol.21 , pp. 119-144
    • Ehrnfeucht, A.1    Kerhumäki, J.2    Rozenberg, G.3
  • 26
    • 0005274241 scopus 로고    scopus 로고
    • Nine test tubes generate any RE language
    • this Vol.
    • C. Ferretti, C. Mauri, C. Zandron, Nine test tubes generate any RE language, Theoret. Comput. Sci. 231 (this Vol.) (2000) 171-180.
    • (2000) Theoret. Comput. Sci. , vol.231 , pp. 171-180
    • Ferretti, C.1    Mauri, C.2    Zandron, C.3
  • 27
    • 0004257896 scopus 로고
    • Goerge Allen & Unwin, London
    • S.W. Golomb, Polyominoes, Goerge Allen & Unwin, London, 1965.
    • (1965) Polyominoes
    • Golomb, S.W.1
  • 28
    • 0040534094 scopus 로고
    • Small universal Minsky machines
    • J. Bečvář (Ed.), Mathematical Foundations of Computer Science, Proc. 8th Symp., Olomouc, Sept. 3-7, 1979
    • Ľ. Gregušová, I. Korec, Small universal Minsky machines, in: J. Bečvář (Ed.), Mathematical Foundations of Computer Science, Proc. 8th Symp., Olomouc, Sept. 3-7, 1979, Lecture Notes in Computer Science, vol. 74, 1979, pp. 308-316.
    • (1979) Lecture Notes in Computer Science , vol.74 , pp. 308-316
    • Gregušová, Ľ.1    Korec, I.2
  • 29
    • 0347540970 scopus 로고
    • Décidabilité et complexité des théories logiques
    • Bruno Courcelle (Ed.), Logique et informatique: une introduction
    • S. Grigorieff, Décidabilité et complexité des théories logiques, in: Bruno Courcelle (Ed.), Logique et informatique: une introduction, Presses de l'INRIA, coll. Didactique, vol. 8, 1991, pp. 7-97.
    • (1991) Presses de L'INRIA, Coll. Didactique , vol.8 , pp. 7-97
    • Grigorieff, S.1
  • 30
    • 0004167145 scopus 로고    scopus 로고
    • International Thomson Computer Press, Boston
    • J. Gruska, Foundations of Computing, International Thomson Computer Press, Boston, 1997.
    • (1997) Foundations of Computing
    • Gruska, J.1
  • 31
    • 0011006633 scopus 로고    scopus 로고
    • Word problems for certain classes of semi-groups
    • Russian
    • Yu. Gurevich, Word problems for certain classes of semi-groups, Algebra i Logika 5 (5) (1996) 25-35 (Russian).
    • (1996) Algebra i Logika , vol.5 , Issue.5 , pp. 25-35
    • Gurevich, Yu.1
  • 32
    • 0002526117 scopus 로고
    • Conway's prime producing machine
    • R.K. Guy, Conway's prime producing machine, Math. Mag. 56 (1) (1983) 26-33.
    • (1983) Math. Mag. , vol.56 , Issue.1 , pp. 26-33
    • Guy, R.K.1
  • 33
    • 0023494703 scopus 로고
    • Formal language theory and DNA: An analysis of the generative capacity of recombinant behaviors
    • T. Head, Formal language theory and DNA: an analysis of the generative capacity of recombinant behaviors, Bull. Math. Biol. 49 (1987) 737-759.
    • (1987) Bull. Math. Biol. , vol.49 , pp. 737-759
    • Head, T.1
  • 37
    • 84947803525 scopus 로고
    • Optimal Simulation of Automata by Neural Nets
    • P. Indyk, Optimal Simulation of Automata by Neural Nets, Lecture Notes in Computer Science, vol. 900, 1995, pp. 337-348.
    • (1995) Lecture Notes in Computer Science , vol.900 , pp. 337-348
    • Indyk, P.1
  • 38
    • 0001058248 scopus 로고
    • Universal diophantine equation
    • J.P. Jones, Universal diophantine equation, J. Symbolic Logic 47 (3) (1982) 549-571.
    • (1982) J. Symbolic Logic , vol.47 , Issue.3 , pp. 549-571
    • Jones, J.P.1
  • 39
    • 0347685887 scopus 로고    scopus 로고
    • Using DNA to solve the Bounded Post Correspondence Problem
    • this Vol.
    • L. Kari, G. Gloor, S. Yu, Using DNA to solve the Bounded Post Correspondence Problem, Theoret. Comput. Sci. 231 (this Vol.) (2000) 193-203.
    • (2000) Theoret. Comput. Sci. , vol.231 , pp. 193-203
    • Kari, L.1    Gloor, G.2    Yu, S.3
  • 40
    • 0346375566 scopus 로고
    • Small universal one-state linear operator algorithm
    • Proc. MFCS'92, Prague, Aug. 21-28
    • F. Kaščák, Small universal one-state linear operator algorithm, Proc. MFCS'92, Prague, Aug. 21-28, Lecture Notes in Computer Science, vol. 629, 1992, pp. 327-335.
    • (1992) Lecture Notes in Computer Science , vol.629 , pp. 327-335
    • Kaščák, F.1
  • 41
    • 0003067817 scopus 로고
    • Representation of events in nerve nets and finite automata
    • C. Shannon, J. McCarthy (Eds.), Princeton University Press, Princeton, NJ
    • S.C. Kleene, Representation of events in nerve nets and finite automata, in: C. Shannon, J. McCarthy (Eds.), Automata Studies, Princeton University Press, Princeton, NJ, 1956, pp. 3-41.
    • (1956) Automata Studies , pp. 3-41
    • Kleene, S.C.1
  • 43
    • 0346910197 scopus 로고
    • A density estimate for the 3x+1 problem
    • I. Korec, A density estimate for the 3x+1 problem, Math. Slovaca 44 (1) (1994) 85-89.
    • (1994) Math. Slovaca , vol.44 , Issue.1 , pp. 85-89
    • Korec, I.1
  • 44
    • 0030283937 scopus 로고    scopus 로고
    • Small universal register machines
    • Theoret. Comput. Sci. 168-2
    • I. Korec, Small universal register machines, Theoret. Comput. Sci. 168-2, special issue on Univ. Mach. Comput. (1996), 267-301.
    • (1996) Univ. Mach. Comput. , Issue.SPEC. ISSUE , pp. 267-301
    • Korec, I.1
  • 45
    • 0030284012 scopus 로고    scopus 로고
    • Small deterministic turing machines
    • Theoret. Comput. Sci. 168-2
    • M. Kudlek, Small deterministic turing machines, Theoret. Comput. Sci. 168-2, special issue on Univ. Mach. Comput. (1996) 241-255.
    • (1996) Univ. Mach. Comput. , Issue.SPEC. ISSUE , pp. 241-255
    • Kudlek, M.1
  • 46
    • 0002747273 scopus 로고
    • The 3x + 1 problem and its generalisations
    • J.C. Lagarias, The 3x + 1 problem and its generalisations, Amer. Math. Mon. 92 (1985) 3-23.
    • (1985) Amer. Math. Mon. , vol.92 , pp. 3-23
    • Lagarias, J.C.1
  • 47
    • 37349120648 scopus 로고
    • The 3x+1 problem and its generalisations
    • J. Borwein et al. (Eds.), Organic Mathematics. Burnaby, Canada, Dec. 12-14, 1995, AMS, Providence, RI. ISBN 0-8218-0668-8
    • J.C. Lagarias, The 3x+1 problem and its generalisations, in: J. Borwein et al. (Eds.), Organic Mathematics. Proc. Workshop Simon Fraser Univ., Burnaby, Canada, Dec. 12-14, 1995, AMS, Providence, RI. ISBN 0-8218-0668-8, 1995. available at: http://www.cecm.sfu.ca/organics/papers/lagarias/
    • (1995) Proc. Workshop Simon Fraser Univ.
    • Lagarias, J.C.1
  • 48
    • 0001223260 scopus 로고
    • Universal computation in simple one-dimensional cellular automata
    • K. Lindgren, M.G. Nordahl, Universal computation in simple one-dimensional cellular automata, Complex Systems 4 (1990) 299-318.
    • (1990) Complex Systems , vol.4 , pp. 299-318
    • Lindgren, K.1    Nordahl, M.G.2
  • 49
    • 51249194645 scopus 로고
    • A logical calculus of the ideas immanent in nervous activity
    • W. S. McCulloch, W. Pitts, A logical calculus of the ideas immanent in nervous activity, Bull. Math. Biophys. 5 (1943) 115-133.
    • (1943) Bull. Math. Biophys. , vol.5 , pp. 115-133
    • McCulloch, W.S.1    Pitts, W.2
  • 50
    • 0000331030 scopus 로고
    • Das Identitätsproblem für Gruppen mit einer defineirenden
    • W. Magnus, Das Identitätsproblem für Gruppen mit einer defineirenden, Relation. Math. Ann. 106 (1932) 295-307.
    • (1932) Relation. Math. Ann. , vol.106 , pp. 295-307
    • Magnus, W.1
  • 51
    • 21144465595 scopus 로고
    • Turing machines: On the frontier between a decidable halting problem and universality
    • Proc. FCT'93
    • M. Margenstern, Turing machines: on the frontier between a decidable halting problem and universality, Lecture Notes in Computer Science, vol. 710, in Proc. FCT'93, 1993, pp. 375-385.
    • (1993) Lecture Notes in Computer Science , vol.710 , pp. 375-385
    • Margenstern, M.1
  • 52
    • 84955574478 scopus 로고
    • Non-erasing Turing machines: A new frontier between a decidable halting problem and universality
    • Proc. LATIN'95
    • M. Margenstern, Non-erasing Turing machines: a new frontier between a decidable halting problem and universality, Lecture Notes in Computer Science, vol. 911, in Proc. LATIN'95, 1995, pp. 386-397.
    • (1995) Lecture Notes in Computer Science , vol.911 , pp. 386-397
    • Margenstern, M.1
  • 53
    • 0347540971 scopus 로고
    • Results on the halting problem
    • Florence, August
    • M. Margenstern, Results on the halting problem, LMPS'95 Internat. Conf, Florence, August 1995.
    • (1995) LMPS'95 Internat. Conf
    • Margenstern, M.1
  • 54
    • 0031521878 scopus 로고    scopus 로고
    • The laterality problem for non-erasing Turing machines on {0, 1} is completely solved, RAIRO
    • M. Margenstern, The laterality problem for non-erasing Turing machines on {0, 1} is completely solved, RAIRO, Theoret. Inform. Appl. 31 (2) (1997) 159-204.
    • (1997) Theoret. Inform. Appl. , vol.31 , Issue.2 , pp. 159-204
    • Margenstern, M.1
  • 55
    • 21744452251 scopus 로고    scopus 로고
    • Decidability and undecidability of the halting problem on turing machines, a survey
    • Proc. LFCS
    • M. Margenstern, Decidability and undecidability of the halting problem on turing machines, a survey, Lecture Notes in Computer Science, vol. 1234, in Proc. LFCS' 1997, pp. 226-236.
    • (1997) Lecture Notes in Computer Science , vol.1234 , pp. 226-236
    • Margenstern, M.1
  • 56
    • 0038396811 scopus 로고    scopus 로고
    • Frontier between decidability and undecidability: A survey
    • ISBN 2-9511539-2-9
    • M. Margenstern, Frontier between decidability and undecidability: a survey, Proc. MCU'98, vol. I, ISBN 2-9511539-2-9, 1998, pp. 141-177.
    • (1998) Proc. MCU'98 , vol.1 , pp. 141-177
    • Margenstern, M.1
  • 61
    • 0020496097 scopus 로고
    • Physics-like models of computation
    • N. Margolus, Physics-like models of computation, Physica 10D (1984) 81-95.
    • (1984) Physica , vol.10 D , pp. 81-95
    • Margolus, N.1
  • 62
    • 34250882960 scopus 로고
    • On the impossiblity of certain algorithms in the theory of associative sytems
    • A.A. Markov, On the impossiblity of certain algorithms in the theory of associative sytems, Dokl. Akad. Nauk SSSR 55 (1947) 583-586.
    • (1947) Dokl. Akad. Nauk SSSR , vol.55 , pp. 583-586
    • Markov, A.A.1
  • 63
    • 0346279934 scopus 로고
    • On E.L. Post's "Tag" problem
    • S.Yu. Maslov, On E.L. Post's "Tag" problem, Trudy Mat. Inst. im. Steklova 72 (1964) 57-68 (English transl. Amer. Math. Soc. Transl. Ser. 2 97 (1971) 1-14).
    • (1964) Trudy Mat. Inst. Im. Steklova , vol.72 , pp. 57-68
    • Maslov, S.Yu.1
  • 64
    • 84865762683 scopus 로고
    • S.Yu. Maslov, On E.L. Post's "Tag" problem, Trudy Mat. Inst. im. Steklova 72 (1964) 57-68 (English transl. Amer. Math. Soc. Transl. Ser. 2 97 (1971) 1-14).
    • (1971) Amer. Math. Soc. Transl. Ser. 2 , vol.97 , pp. 1-14
  • 65
    • 37349064371 scopus 로고
    • Certain properties of E.L. Post's apparatus of canonical calculi
    • S.Yu. Maslov, Certain properties of E.L. Post's apparatus of canonical calculi, Trudy Mat. Inst. im. Steklova 72 (1964) 5-56 (English transl. Amer. Math. Soc. Transl. ser. 2 98 (1971) 91-161).
    • (1964) Trudy Mat. Inst. Im. Steklova , vol.72 , pp. 5-56
    • Maslov, S.Yu.1
  • 66
    • 0347540969 scopus 로고
    • S.Yu. Maslov, Certain properties of E.L. Post's apparatus of canonical calculi, Trudy Mat. Inst. im. Steklova 72 (1964) 5-56 (English transl. Amer. Math. Soc. Transl. ser. 2 98 (1971) 91-161).
    • (1971) Amer. Math. Soc. Transl. Ser. 2 , vol.98 , pp. 91-161
  • 67
    • 0346279935 scopus 로고
    • Simple examples of unsolvable canonical calculi
    • Yu.V. Matiyasevich, Simple examples of unsolvable canonical calculi, Trudy MIAN 93 (1967) 50-88 (English transl. Proc. Steklov Inst. Math. (1970), 61-110).
    • (1967) Trudy MIAN , vol.93 , pp. 50-88
    • Matiyasevich, Yu.V.1
  • 68
    • 0347540964 scopus 로고
    • Yu.V. Matiyasevich, Simple examples of unsolvable canonical calculi, Trudy MIAN 93 (1967) 50-88 (English transl. Proc. Steklov Inst. Math. (1970), 61-110).
    • (1970) Proc. Steklov Inst. Math. , pp. 61-110
  • 69
    • 0039939857 scopus 로고
    • Simple examples of unsolvable canonical calculi
    • Yu.V. Matiyasevich, Simple examples of unsolvable canonical calculi, D.A.N. SSSR 173 (6) (1967) 1264-1266.
    • (1967) D.A.N. SSSR , vol.173 , Issue.6 , pp. 1264-1266
    • Matiyasevich, Yu.V.1
  • 70
    • 77956959215 scopus 로고
    • On recursive unsolvability of Hilbert's Tenth Problem
    • P. Suppes, L. Henkin, A. Joja, Gr. C. Moisil (Eds.), Logic, Methodology and Philosophy of Science IV
    • Yu.V. Matiyasevich, On recursive unsolvability of Hilbert's Tenth Problem, in: P. Suppes, L. Henkin, A. Joja, Gr. C. Moisil (Eds.), Logic, Methodology and Philosophy of Science IV, Studies in Logic and Foundations of Mathematics, vol. 74, 1973, pp. 89-110.
    • (1973) Studies in Logic and Foundations of Mathematics , vol.74 , pp. 89-110
    • Matiyasevich, Yu.V.1
  • 71
    • 0348170714 scopus 로고
    • On investigations on some algorithmic problems in algebra and number theory
    • Yu.V. Matiyasevich, On investigations on some algorithmic problems in algebra and number theory, Trudy Mat. Inst. im. Steklova 168 (1984) 218-235 (English transl. Proc. Steklov Inst. Math. 3 (1986) 227-252).
    • (1984) Trudy Mat. Inst. Im. Steklova , vol.168 , pp. 218-235
    • Matiyasevich, Yu.V.1
  • 72
    • 0346279933 scopus 로고
    • Yu.V. Matiyasevich, On investigations on some algorithmic problems in algebra and number theory, Trudy Mat. Inst. im. Steklova 168 (1984) 218-235 (English transl. Proc. Steklov Inst. Math. 3 (1986) 227-252).
    • (1986) Proc. Steklov Inst. Math. , vol.3 , pp. 227-252
  • 73
    • 0004269968 scopus 로고
    • Nauka Publishers, Fizmatlit, 1993 Russian; English translation: MIT Press, Cambridge, MA
    • Yu.V. Matiyasevich, Hilbert's Tenth Problem, Nauka Publishers, Fizmatlit, 1993 (Russian; English translation: MIT Press, Cambridge, MA, 1993).
    • (1993) Hilbert's Tenth Problem
    • Matiyasevich, Yu.V.1
  • 74
    • 85037512418 scopus 로고    scopus 로고
    • Universal polynomials
    • ISBN 2-9511539-2-9
    • Yu.V. Matiyasevich, Universal polynomials, Proc. MCU'98, vol. I, ISBN 2-9511539-2-9, 1998, pp. 1-20.
    • (1998) Proc. MCU'98 , vol.1 , pp. 1-20
    • Matiyasevich, Yu.V.1
  • 75
    • 0029696236 scopus 로고    scopus 로고
    • Decision problems for semi-Thue systems with a few rules
    • IEEE Computer Society Press, Silverspring, MD
    • Yu.V. Matiyasevich, G. Sénizergues, Decision problems for semi-Thue systems with a few rules, Proc. LICS'96, IEEE Computer Society Press, Silverspring, MD, 1996, pp. 523-531.
    • (1996) Proc. LICS'96 , pp. 523-531
    • Matiyasevich, Yu.V.1    Sénizergues, G.2
  • 76
    • 85037518432 scopus 로고    scopus 로고
    • Decision problems for semi-Thue systems with a few rules
    • ISBN 2-9511539-0-2
    • Yu.V. Matiyasevich, G. Sénizergues, Decision problems for semi-Thue systems with a few rules, Proc. JAF13, ISBN 2-9511539-0-2, 1997, pp. 137-166.
    • (1997) Proc. JAF13 , pp. 137-166
    • Matiyasevich, Yu.V.1    Sénizergues, G.2
  • 77
    • 2142746675 scopus 로고
    • Busy beaver competition and Collatz-like problems
    • P. Michel, Busy beaver competition and Collatz-like problems, Arch. Math. Logic 32 (1993) 351-367.
    • (1993) Arch. Math. Logic , vol.32 , pp. 351-367
    • Michel, P.1
  • 79
    • 0347244231 scopus 로고    scopus 로고
    • Self-reproduction in a reversible cellular space
    • Theoret. Comput. Sci. 168-2
    • K. Morita, K. Imai, Self-reproduction in a reversible cellular space, Theoret. Comput. Sci. 168-2, special issue on Univ. Mach. Comput. (1996) 303-320.
    • (1996) Univ. Mach. Comput. , Issue.SPEC. ISSUE , pp. 303-320
    • Morita, K.1    Imai, K.2
  • 80
    • 84958596690 scopus 로고    scopus 로고
    • Logical universality and self-reproduction in reversible cellular automata
    • Proc. 1st Internat. Conf. on Evolvable Systems, Tsukuba, Springer, Berlin
    • K. Morita, K. Imai, Logical universality and self-reproduction in reversible cellular automata, Proc. 1st Internat. Conf. on Evolvable Systems, Tsukuba, Lecture Notes in Computer Science, vol. 1259, Springer, Berlin, 1996, pp. 152-166.
    • (1996) Lecture Notes in Computer Science , vol.1259 , pp. 152-166
    • Morita, K.1    Imai, K.2
  • 81
    • 0347540959 scopus 로고    scopus 로고
    • A simple self-reproducing cellular automaton with shape-encoding mechanism
    • C.G. Langton, K. Shimohara (Eds.), MIT Press, Cambridge, MA
    • K. Morita, K. Imai, A simple self-reproducing cellular automaton with shape-encoding mechanism, in: C.G. Langton, K. Shimohara (Eds.), Artificial Life V, MIT Press, Cambridge, MA, 1997, pp. 489-496.
    • (1997) Artificial Life V , vol.5 , pp. 489-496
    • Morita, K.1    Imai, K.2
  • 82
    • 0002996665 scopus 로고
    • On the algorithmic unsolvability of the word problem in group theory
    • P.S. Novikov, On the algorithmic unsolvability of the word problem in group theory, Trudy Mat. Inst. im. Steklova 44 (1955) (English translation in Amer. Math. Soc. Transl. 9 (2) (1958)).
    • (1955) Trudy Mat. Inst. Im. Steklova , vol.44
    • Novikov, P.S.1
  • 83
    • 0347540962 scopus 로고
    • P.S. Novikov, On the algorithmic unsolvability of the word problem in group theory, Trudy Mat. Inst. im. Steklova 44 (1955) (English translation in Amer. Math. Soc. Transl. 9 (2) (1958)).
    • (1958) Amer. Math. Soc. Transl. , vol.9 , Issue.2
  • 84
    • 0346279929 scopus 로고
    • The caracterization of tag-systems in term of decidability
    • D. Pager, The caracterization of tag-systems in term of decidability, J. London Math. Soc. 2 (2) (1970) 473-480.
    • (1970) J. London Math. Soc. , vol.2 , Issue.2 , pp. 473-480
    • Pager, D.1
  • 85
    • 0042452747 scopus 로고
    • A note on Post's correspondance problem
    • J.-J. Pansiot, A note on Post's correspondance problem, Inform. Process. Lett. 12 (5) (1981) 233.
    • (1981) Inform. Process. Lett. , vol.12 , Issue.5 , pp. 233
    • Pansiot, J.-J.1
  • 86
    • 0346910260 scopus 로고    scopus 로고
    • DNA computing: Distributed splicing systems
    • Structures in Logic and Computer Science, A Selection of Essays in Honor of A. Ehrenfeucht, Springer, Berlin
    • G. Pǎun, DNA computing: distributed splicing systems, in Structures in Logic and Computer Science, A Selection of Essays in Honor of A. Ehrenfeucht, Lecture Notes in Computer Science, vol. 1261, Springer, Berlin, 1997, pp. 353-370.
    • (1997) Lecture Notes in Computer Science , vol.1261 , pp. 353-370
    • Pǎun, G.1
  • 87
    • 0005278537 scopus 로고    scopus 로고
    • DNA computing based on splicing: Universality results
    • this Vol.
    • G. Pǎun, DNA computing based on splicing: universality results, Theoret. Comput. Sci. 231 (this Vol.) (2000) 275-296.
    • (2000) Theoret. Comput. Sci. , vol.231 , pp. 275-296
    • Pǎun, G.1
  • 88
    • 0030291381 scopus 로고    scopus 로고
    • Computing by splicing
    • Theoret. Comput. Sci. 168-2
    • G. Pǎun, G. Rozenberg, A. Salomaa, Computing by splicing, Theoret. Comput. Sci. 168-2, special issue on Univ. Mach. Comput. (1996) 321-336.
    • (1996) Univ. Mach. Comput. , Issue.SPEC. ISSUE , pp. 321-336
    • Pǎun, G.1    Rozenberg, G.2    Salomaa, A.3
  • 89
    • 0004455009 scopus 로고
    • Razreshimost' problemy ostanovki dlja nekotorykh klassov mashin T'juringa
    • Ijun
    • L.M. Pavlotskaya, Razreshimost' problemy ostanovki dlja nekotorykh klassov mashin T'juringa, Matematicheskie Zametki 13 (6) (1973) 899-909, Ijun' (transl. Solvability of the halting problem for certain classes of Turing machines, Notes of the Acad. Sci. USSR 13 (6) (1973) 537-541).
    • (1973) Matematicheskie Zametki , vol.13 , Issue.6 , pp. 899-909
    • Pavlotskaya, L.M.1
  • 90
    • 0038097288 scopus 로고
    • Solvability of the halting problem for certain classes of Turing machines
    • L.M. Pavlotskaya, Razreshimost' problemy ostanovki dlja nekotorykh klassov mashin T'juringa, Matematicheskie Zametki 13 (6) (1973) 899-909, Ijun' (transl. Solvability of the halting problem for certain classes of Turing machines, Notes of the Acad. Sci. USSR 13 (6) (1973) 537-541).
    • (1973) Notes of the Acad. Sci. USSR , vol.13 , Issue.6 , pp. 537-541
  • 91
    • 0038436248 scopus 로고
    • O minimal'nom chisle razlichnykh kodov vershin v grafe universal'noj mashiny T'juringa, Diskretnyj analiz
    • in Russian
    • L.M. Pavlotskaya, O minimal'nom chisle razlichnykh kodov vershin v grafe universal'noj mashiny T'juringa, Diskretnyj analiz, Sb. Tr. Inst. Mat. SO AN SSSR 27 (1975) 52-60 (On the minimal number of distinct codes for the vertices of the graph of a universal Turing machine) (in Russian)
    • (1975) Sb. Tr. Inst. Mat. SO AN SSSR , vol.27 , pp. 52-60
    • Pavlotskaya, L.M.1
  • 92
    • 0348170709 scopus 로고
    • Dostatochnye uslovija razreshimosti problemy ostanovki dlja mashin T'juring
    • in Russian
    • L.M. Pavlotskaya, Dostatochnye uslovija razreshimosti problemy ostanovki dlja mashin T'juring, Avtomaty i mashiny (1978) 91-118 (Sufficient conditions for halting problem decidability of Turing machines) (in Russian).
    • (1978) Avtomaty i Mashiny , pp. 91-118
    • Pavlotskaya, L.M.1
  • 93
    • 0030284980 scopus 로고    scopus 로고
    • On machines, universal by extensions
    • Theoret. Comput. Sci. 168-2
    • L.M. Pavlotskaya, On machines, universal by extensions, Theoret. Comput. Sci. 168-2, special issue on Univ. Mach. Comput. (1996) 257-266.
    • (1996) Univ. Mach. Comput. , Issue.SPEC. ISSUE , pp. 257-266
    • Pavlotskaya, L.M.1
  • 94
    • 0003688270 scopus 로고
    • Oxford University Press, Oxford, 466p.
    • R. Penrose, The Emperor's New Mind, Oxford University Press, Oxford, 1989, 466p.
    • (1989) The Emperor's New Mind
    • Penrose, R.1
  • 96
    • 0002605406 scopus 로고
    • Recursive unsolvability of a problem of Thue
    • E.L. Post, Recursive unsolvability of a problem of Thue, J. Symbolic Logic 12 (1947) 1-11.
    • (1947) J. Symbolic Logic , vol.12 , pp. 1-11
    • Post, E.L.1
  • 97
    • 0344769962 scopus 로고
    • Towards a precise characterization of the complexity of universal and nonuniversal Turing machines
    • L. Priese, Towards a precise characterization of the complexity of universal and nonuniversal Turing machines, SIAM J. Comput. 8 (4) (1979) 508-523.
    • (1979) SIAM J. Comput. , vol.8 , Issue.4 , pp. 508-523
    • Priese, L.1
  • 98
    • 0345632403 scopus 로고    scopus 로고
    • Finite H-Systems with 3 Test Tubes are not Predictable
    • Kapalua, Maui, January 1998. - Hawaii, USA
    • L. Priese, Yu. Rogozhin, M. Margenstern, Finite H-Systems with 3 Test Tubes are not Predictable, in Proc. Pacific Symp. on Biocomputing, Kapalua, Maui, January 1998. - Hawaii, USA, 1998, 545-556.
    • (1998) Proc. Pacific Symp. on Biocomputing , pp. 545-556
    • Priese, L.1    Rogozhin, Yu.2    Margenstern, M.3
  • 99
    • 0000536874 scopus 로고
    • Undecidability and nonperiodicity for tilings of the plane
    • R.M. Robinson, Undecidability and nonperiodicity for tilings of the plane, Invent. Math. 12 (1971) 177-209.
    • (1971) Invent. Math. , vol.12 , pp. 177-209
    • Robinson, R.M.1
  • 100
    • 0001646410 scopus 로고
    • Undecidable tiling problems in the hyperbolic plane
    • R.M. Robinson, Undecidable tiling problems in the hyperbolic plane, Invent. Math. 44 (1978) 259-264.
    • (1978) Invent. Math. , vol.44 , pp. 259-264
    • Robinson, R.M.1
  • 101
    • 0004477834 scopus 로고
    • Sem' universal'nykh mashin T'juringa
    • in Russian
    • Ju.V. Rogozhin, Sem' universal'nykh mashin T'juringa, Mat. Issledovanija 69 (1982) 76-90 (Seven universal Turing machines) (in Russian).
    • (1982) Mat. Issledovanija , vol.69 , pp. 76-90
    • Rogozhin, Ju.V.1
  • 102
    • 0004477834 scopus 로고
    • Universal'naja mashina T'juringa s 10 sostojanijami i 3 simvolami
    • in Russian
    • Ju.V. Rogozhin, Universal'naja mashina T'juringa s 10 sostojanijami i 3 simvolami, Mate. Issledovanija 69 (1992) 76-90 (A universal Turing machine with 10 states and 3 symbols) (in Russian).
    • (1992) Mate. Issledovanija , vol.69 , pp. 76-90
    • Rogozhin, Ju.V.1
  • 103
    • 0030286377 scopus 로고    scopus 로고
    • Small universal Turing machines
    • Theoret. Comput. Sci. 168-2
    • Ju.V. Rogozhin, Small universal Turing machines, Theoret. Comput. Sci. 168-2, special issue on Univ. Mach. Comput. (1996) 215-240.
    • (1996) Univ. Mach. Comput. , Issue.SPEC. ISSUE , pp. 215-240
    • Rogozhin, Ju.V.1
  • 104
    • 0004482757 scopus 로고    scopus 로고
    • A Universal Turing machine with 22 States and 2 Symbols
    • Ju.V. Rogozhin, A Universal Turing machine with 22 States and 2 Symbols, Romanian J. Inform. Sci. Technol. 1 (3) (1998) 259-265.
    • (1998) Romanian J. Inform. Sci. Technol. , vol.1 , Issue.3 , pp. 259-265
    • Rogozhin, Ju.V.1
  • 105
    • 21844491945 scopus 로고
    • Simulations between cellular automata on Cayley graphs
    • Latin American Theoretical INformatics '95
    • Zs. Roka, Simulations between cellular automata on Cayley graphs, Latin American Theoretical INformatics '95, Lecture Notes in Computer Science, vol. 911, 1995, pp. 483-493.
    • (1995) Lecture Notes in Computer Science , vol.911 , pp. 483-493
    • Roka, Zs.1
  • 106
    • 0039812500 scopus 로고
    • A short recursively unsolvable problem
    • D. Scott, A short recursively unsolvable problem, J. Symbolic Logic 21 (1956) 111-112.
    • (1956) J. Symbolic Logic , vol.21 , pp. 111-112
    • Scott, D.1
  • 107
    • 0004391721 scopus 로고    scopus 로고
    • L(A) = L(B)?
    • Proc. INFINITY 97
    • G. Sénizergues, L(A) = L(B)? Proc. INFINITY 97, Electronic Notes in Computer Sciences, vol. 9, 1997, pp. 1-26. available at: http://www.elsevier.nl/locate/entcs/volume9.html
    • (1997) Electronic Notes in Computer Sciences , vol.9 , pp. 1-26
    • Sénizergues, G.1
  • 108
    • 84951060219 scopus 로고    scopus 로고
    • The equivalence problem for deterministic pushdown automata is decidable
    • Proc. ICALP '97
    • G. Sénizergues, The equivalence problem for deterministic pushdown automata is decidable, Proc. ICALP '97, Lecture Notes in Computer Science, vol. 1256, 1997, pp. 671-681.
    • (1997) Lecture Notes in Computer Science , vol.1256 , pp. 671-681
    • Sénizergues, G.1
  • 109
    • 0346929351 scopus 로고    scopus 로고
    • Complete formal systems for equivalence problems
    • this Vol.
    • G. Sénizergues, Complete formal systems for equivalence problems, Theoret. Comput. Sci. (this Vol.) (2000) 309-334.
    • (2000) Theoret. Comput. Sci. , pp. 309-334
    • Sénizergues, G.1
  • 110
    • 0023331659 scopus 로고
    • Three-state Neumann neighbour cellular automata capable of constructing self-reproducing machines
    • T. Serizawa, Three-state Neumann neighbour cellular automata capable of constructing self-reproducing machines, Systems Comput. Jpn 18 (4) (1987) 33-40.
    • (1987) Systems Comput. Jpn , vol.18 , Issue.4 , pp. 33-40
    • Serizawa, T.1
  • 111
    • 0001426220 scopus 로고
    • A universal Turing machine with two internal states
    • C.E. Shannon, A universal Turing machine with two internal states, Ann. Math. Stud. 34 (1956) 157-165.
    • (1956) Ann. Math. Stud. , vol.34 , pp. 157-165
    • Shannon, C.E.1
  • 112
    • 0002663413 scopus 로고
    • Turing computability with neural nets
    • H.T. Siegelmann, E.D. Sontag, Turing computability with neural nets, Appl. Math. Lett. 4 (6) (1991) 77-80.
    • (1991) Appl. Math. Lett. , vol.4 , Issue.6 , pp. 77-80
    • Siegelmann, H.T.1    Sontag, E.D.2
  • 114
    • 0000745182 scopus 로고
    • Computation and construction universality of reversible cellular automata
    • T. Toffoli, Computation and construction universality of reversible cellular automata, J. Comput. Systems Sci. 15 (2) (1977) 213-231.
    • (1977) J. Comput. Systems Sci. , vol.15 , Issue.2 , pp. 213-231
    • Toffoli, T.1
  • 115
    • 0346910189 scopus 로고
    • An associative calculus with an unsolvable problem of equivalence
    • G.S. Tsejtin, An associative calculus with an unsolvable problem of equivalence, Trudy Mat. Nauk Steklova 52 (1958) (English transl. AMS Transl. 94 (1970) 73-92).
    • (1958) Trudy Mat. Nauk Steklova , vol.52
    • Tsejtin, G.S.1
  • 116
    • 0346279925 scopus 로고
    • G.S. Tsejtin, An associative calculus with an unsolvable problem of equivalence, Trudy Mat. Nauk Steklova 52 (1958) (English transl. AMS Transl. 94 (1970) 73-92).
    • (1970) AMS Transl. , vol.94 , pp. 73-92
  • 117
    • 84960561455 scopus 로고
    • On computable real numbers, with an application to the Entscheidungsproblem
    • A.M. Turing, On computable real numbers, with an application to the Entscheidungsproblem, Proc. London Math. Soc. Ser. 2 42 (1936) 230-265.
    • (1936) Proc. London Math. Soc. Ser. 2 , vol.42 , pp. 230-265
    • Turing, A.M.1
  • 119
  • 120
  • 121
    • 0342976580 scopus 로고
    • A variant to Turing's theory of computing machines
    • H. Wang, A variant to Turing's theory of computing machines, J. Assoc. Comput. Mach. 4 (1957) 63-92.
    • (1957) J. Assoc. Comput. Mach. , vol.4 , pp. 63-92
    • Wang, H.1
  • 122
    • 84944488797 scopus 로고
    • Proving theorems by pattern recognition II
    • H. Wang, Proving theorems by pattern recognition II, Bell Systems Tech. J. 40 (1961) 1-41.
    • (1961) Bell Systems Tech. J. , vol.40 , pp. 1-41
    • Wang, H.1
  • 123
    • 0004455287 scopus 로고
    • Tag systems and lag systems
    • H. Wang, Tag systems and lag systems, Math. Ann. 152 (1963) 65-74.
    • (1963) Math. Ann. , vol.152 , pp. 65-74
    • Wang, H.1
  • 124
    • 0007061086 scopus 로고    scopus 로고
    • Left-divisibility and word problems in single relation monoids
    • G. Watier, Left-divisibility and word problems in single relation monoids, Semigroup Forum 53 (1996) 194-207.
    • (1996) Semigroup Forum , vol.53 , pp. 194-207
    • Watier, G.1
  • 125
    • 0031325242 scopus 로고    scopus 로고
    • On the word problem for single relation monoids with an unbordered relator
    • G. Watier, On the word problem for single relation monoids with an unbordered relator, Internat. J. Algebraic Comput. 7 (6) (1997) 749-770.
    • (1997) Internat. J. Algebraic Comput. , vol.7 , Issue.6 , pp. 749-770
    • Watier, G.1
  • 126
    • 0348170659 scopus 로고
    • Remarks about a theorem of hao Wang
    • G.P. Zykin, Remarks about a theorem of hao Wang, Algebra i Logika 2 (1963) 33-35.
    • (1963) Algebra i Logika , vol.2 , pp. 33-35
    • Zykin, G.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.