메뉴 건너뛰기




Volumn 209, Issue 3, 2011, Pages 456-470

Descriptional and computational complexity of finite automata - A survey

Author keywords

Alternation; Computational complexity; Descriptional complexity; Determinism; Finite automata; Nondeterminism; Survey

Indexed keywords

ALTERNATION; DESCRIPTIONAL COMPLEXITY; DETERMINISM; NON-DETERMINISM; REGULAR LANGUAGES;

EID: 79751524882     PISSN: 08905401     EISSN: 10902651     Source Type: Journal    
DOI: 10.1016/j.ic.2010.11.013     Document Type: Article
Times cited : (147)

References (88)
  • 1
    • 33746220960 scopus 로고    scopus 로고
    • Some descriptional complexity problems in finite automata theory
    • Computing Society of the Philippines
    • H.N. Adorna Some descriptional complexity problems in finite automata theory Philippine Computing Science Congress (PCSC 2005) 2005 Computing Society of the Philippines
    • (2005) Philippine Computing Science Congress (PCSC 2005)
    • Adorna, H.N.1
  • 3
    • 38049091720 scopus 로고
    • A very hard log-space counting class
    • C. Álvarez, and B. Jenner A very hard log-space counting class Theoret. Comput. Sci. 107 1993 3 30
    • (1993) Theoret. Comput. Sci. , vol.107 , pp. 3-30
    • Álvarez, C.1    Jenner, B.2
  • 4
    • 0002970176 scopus 로고
    • 1 formulae on finite structures
    • 1 formulae on finite structures Ann. Pure. Appl. Logic 24 1983 1 48
    • (1983) Ann. Pure. Appl. Logic , vol.24 , pp. 1-48
    • Ajtai, M.1
  • 5
    • 84974730838 scopus 로고    scopus 로고
    • FA Minimisation Heuristics for a Class of Finite Languages
    • Automata Implementation
    • J. Amilhastre, P. Janssen, and M.C. Vilarem FA minimisation heuristics for a class of finite languages Workshop on Implementing Automata (WIA 2001) LNCS vol. 2214 2001 Springer 1 12 (Pubitemid 33359640)
    • (2001) LNCS , Issue.2214 , pp. 1-12
    • Amilhastre, J.1    Janssen, P.2    Vilarem, M.-C.3
  • 7
    • 0024606026 scopus 로고
    • Bounded-width polynomial-size branching programs recognize exactly those languages in NC 1
    • D.A. Barrington Bounded-width polynomial-size branching programs recognize exactly those languages in NC 1 J. Comput. System Sci. 38 1989 150 164
    • (1989) J. Comput. System Sci. , vol.38 , pp. 150-164
    • Barrington, D.A.1
  • 9
    • 0024092214 scopus 로고
    • Finite monoids and the fine structure of NC 1
    • D.M. Barrington, and D. Thérien Finite monoids and the fine structure of NC 1 J. ACM 35 1988 941 952
    • (1988) J. ACM , vol.35 , pp. 941-952
    • Barrington, D.M.1    Thérien, D.2
  • 10
    • 0000392751 scopus 로고
    • Intersection and union of regular languages and state complexity
    • J.C. Birget Intersection and union of regular languages and state complexity Inform. Process. Lett. 43 1992 85 190
    • (1992) Inform. Process. Lett. , vol.43 , pp. 85-190
    • Birget, J.C.1
  • 11
    • 49049121424 scopus 로고    scopus 로고
    • The tractability frontier for NFA minimization
    • Springer, International Colloqium on Automata, Languages and Programming (ICALP 2008)
    • H. Björklund, and W. Martens The tractability frontier for NFA minimization International Colloqium on Automata, Languages and Programming (ICALP 2008) LNCS vol. 5126 2008 Springer 27 38
    • (2008) LNCS , vol.5126 , pp. 27-38
    • Björklund, H.1    Martens, W.2
  • 12
    • 67649995916 scopus 로고    scopus 로고
    • Decision problems for convex languages
    • Springer, Language and Automata Theory and Applications (LATA 2009)
    • J. Brzozowski, J. Shallit, and Z. Xu Decision problems for convex languages Language and Automata Theory and Applications (LATA 2009) LNCS vol. 5457 2009 Springer 247 258
    • (2009) LNCS , vol.5457 , pp. 247-258
    • Brzozowski, J.1    Shallit, J.2    Xu, Z.3
  • 13
    • 0002824996 scopus 로고
    • On equations for regular languages, finite automata, and sequential networks
    • J.A. Brzozowski, and E.L. Leiss On equations for regular languages, finite automata, and sequential networks Theoret. Comput. Sci. 10 1980 19 35
    • (1980) Theoret. Comput. Sci. , vol.10 , pp. 19-35
    • Brzozowski, J.A.1    Leiss, E.L.2
  • 15
    • 0026219997 scopus 로고
    • Finite-automaton aperiodicity is PSPACE-complete
    • S. Cho, and D.T. Huynh Finite-automaton aperiodicity is PSPACE-complete Theoret. Comput. Sci. 88 1991 99 116
    • (1991) Theoret. Comput. Sci. , vol.88 , pp. 99-116
    • Cho, S.1    Huynh, D.T.2
  • 16
    • 0026835130 scopus 로고
    • The parallel complexity of finite-state automata problems
    • S. Cho, and D.T. Huynh The parallel complexity of finite-state automata problems Inform. and Comput. 97 1992 1 22
    • (1992) Inform. and Comput. , vol.97 , pp. 1-22
    • Cho, S.1    Huynh, D.T.2
  • 17
    • 0022863896 scopus 로고
    • Finite automata and unary languages
    • M. Chrobak Finite automata and unary languages Theoret. Comput. Sci. 47 1986 149 158
    • (1986) Theoret. Comput. Sci. , vol.47 , pp. 149-158
    • Chrobak, M.1
  • 18
    • 0038238494 scopus 로고    scopus 로고
    • Errata to "finite automata and unary languages"
    • M. Chrobak Errata to "finite automata and unary languages" Theoret. Comput. Sci. 302 2003 497 498
    • (2003) Theoret. Comput. Sci. , vol.302 , pp. 497-498
    • Chrobak, M.1
  • 20
    • 79751525421 scopus 로고
    • The parallel complexity of iterated morphisms and the arithmetic of small numbers
    • Springer, Mathematical Foundations of Computer Science (MFCS 1992)
    • C. Damm, M. Holzer, and K.J. Lange The parallel complexity of iterated morphisms and the arithmetic of small numbers Mathematical Foundations of Computer Science (MFCS 1992) LNCS vol. 629 1992 Springer 227 235
    • (1992) LNCS , vol.629 , pp. 227-235
    • Damm, C.1    Holzer, M.2    Lange, K.J.3
  • 23
    • 0008158848 scopus 로고
    • Constructions for alternating finite automata
    • A. Fellah, H. Jürgensen, and S. Yu Constructions for alternating finite automata Int. J. Comput. Math. 35 1990 117 132
    • (1990) Int. J. Comput. Math. , vol.35 , pp. 117-132
    • Fellah, A.1    Jürgensen, H.2    Yu, S.3
  • 24
    • 0002127588 scopus 로고
    • Parity, circuits, and the polynomial-time hierarchy
    • M.L. Furst, J.B. Saxe, and M. Sipser Parity, circuits, and the polynomial-time hierarchy Math. Systems Theory 17 1984 13 27
    • (1984) Math. Systems Theory , vol.17 , pp. 13-27
    • Furst, M.L.1    Saxe, J.B.2    Sipser, M.3
  • 25
    • 0842283669 scopus 로고
    • Hierarchies of complete problems
    • Z. Galil Hierarchies of complete problems Acta Inform. 6 1976 77 88
    • (1976) Acta Inform. , vol.6 , pp. 77-88
    • Galil, Z.1
  • 27
    • 11844290244 scopus 로고    scopus 로고
    • A lower bound technique for the size of nondeterministic finite automata
    • DOI 10.1016/0020-0190(96)00095-6, PII S0020019096000956
    • I. Glaister, and J. Shallit A lower bound technique for the size of nondeterministic finite automata Inform. Process. Lett. 59 1996 75 77 (Pubitemid 126375635)
    • (1996) Information Processing Letters , vol.59 , Issue.2 , pp. 75-77
    • Glaister, I.1    Shallit, J.2
  • 28
    • 0001187706 scopus 로고
    • Complexity of automaton identification from given data
    • E.M. Gold Complexity of automaton identification from given data Inform. Control 37 1978 302 320
    • (1978) Inform. Control , vol.37 , pp. 302-320
    • Gold, E.M.1
  • 29
    • 33645626080 scopus 로고    scopus 로고
    • Probabilistic and nondeterministic unary automata
    • Mathematical Foundations of Computer Science (MFCS 2003), Springer
    • G. Gramlich Probabilistic and nondeterministic unary automata Mathematical Foundations of Computer Science (MFCS 2003) LNCS vol. 2747 2003 Springer 460 469
    • (2003) LNCS , vol.2747 , pp. 460-469
    • Gramlich, G.1
  • 30
    • 24144466442 scopus 로고    scopus 로고
    • Minimizing NFA's and regular expressions
    • STACS 2005 - 22nd Annual Symposium on Theoretical Aspects of Computer Science, Proceedings
    • G. Gramlich, and G. Schnitger Minimizing NFA's and regular expressions Symposium on Theoretical Aspects of Computer Science (STACS 2005) LNCS vol. 3404 2005 Springer 399 411 (Pubitemid 41241264)
    • (2005) Lecture Notes in Computer Science , vol.3404 , pp. 399-411
    • Gramlich, G.1    Schnitger, G.2
  • 31
    • 0347130415 scopus 로고
    • A note on undecidable properties of formal languages
    • S. Greibach A note on undecidable properties of formal languages Math. Systems Theory 2 1 1968 1 6
    • (1968) Math. Systems Theory , vol.2 , Issue.1 , pp. 1-6
    • Greibach, S.1
  • 36
    • 33750316597 scopus 로고    scopus 로고
    • On Emptiness and Counting for Alternating Finite Automata
    • World Scientific
    • M. Holzer On Emptiness and Counting for Alternating Finite Automata Developments in Language Theory (DLT 1996) 1996 World Scientific pp. 88-97
    • (1996) Developments in Language Theory (DLT 1996)
    • Holzer, M.1
  • 37
    • 11844303665 scopus 로고    scopus 로고
    • Nondeterministic descriptional complexity of regular languages
    • M. Holzer, and M. Kutrib Nondeterministic descriptional complexity of regular languages Int. J. Found. Comput. Sci. 14 2003 1087 1102
    • (2003) Int. J. Found. Comput. Sci. , vol.14 , pp. 1087-1102
    • Holzer, M.1    Kutrib, M.2
  • 38
    • 68649099218 scopus 로고    scopus 로고
    • Nondeterministic finite automata - Recent results on the descriptional and computational complexity
    • M. Holzer, and M. Kutrib Nondeterministic finite automata - recent results on the descriptional and computational complexity Int. J. Found. Comput. Sci. 20 2009 563 580
    • (2009) Int. J. Found. Comput. Sci. , vol.20 , pp. 563-580
    • Holzer, M.1    Kutrib, M.2
  • 39
    • 6344220714 scopus 로고    scopus 로고
    • On the state complexity of k-entry deterministic finite automata
    • M. Holzer, K. Salomaa, and S. Yu On the state complexity of k-entry deterministic finite automata J. Autom. Lang. Comb. 6 2001 453 466
    • (2001) J. Autom. Lang. Comb. , vol.6 , pp. 453-466
    • Holzer, M.1    Salomaa, K.2    Yu, S.3
  • 40
    • 0002197352 scopus 로고
    • An nlogn Algorithm for Minimizing the State in a Finite Automaton
    • Academic Press
    • J. Hopcroft An nlogn Algorithm for Minimizing the State in a Finite Automaton The Theory of Machines and Computations 1971 Academic Press pp. 189-196
    • (1971) The Theory of Machines and Computations
    • Hopcroft, J.1
  • 43
    • 54249086307 scopus 로고    scopus 로고
    • On the hardness of determining small NFA's and of proving lower bounds on their sizesm
    • Developments in Language Theory (DLT 2008), Springer
    • J. Hromkovič, and G. Schnitger On the hardness of determining small NFA's and of proving lower bounds on their sizesm Developments in Language Theory (DLT 2008) LNCS vol. 5257 2008 Springer 34 55
    • (2008) LNCS , vol.5257 , pp. 34-55
    • Hromkovič, J.1    Schnitger, G.2
  • 46
    • 0018678817 scopus 로고
    • Observations on the complexity of regular expressions problems
    • H.B. Hunt III Observations on the complexity of regular expressions problems J. Comput. System Sci. 19 1979 222 236
    • (1979) J. Comput. System Sci. , vol.19 , pp. 222-236
    • Hunt Iii, H.B.1
  • 47
    • 84976739235 scopus 로고
    • On equivalence and contaiment problems for formal languages
    • H.B. Hunt III, and D.J. Rosenkrantz On equivalence and contaiment problems for formal languages J. ACM 24 1977 387 396
    • (1977) J. ACM , vol.24 , pp. 387-396
    • Hunt Iii, H.B.1    Rosenkrantz, D.J.2
  • 48
    • 2342657713 scopus 로고
    • Computational parallels between the regular and context-free languages
    • H.B. Hunt III, and D.J. Rosenkrantz Computational parallels between the regular and context-free languages SIAM J. Comput. 7 1978 99 114
    • (1978) SIAM J. Comput. , vol.7 , pp. 99-114
    • Hunt Iii, H.B.1    Rosenkrantz, D.J.2
  • 49
    • 0016946005 scopus 로고
    • On the equivalence, containment, and covering problems for the regular and context-free languages
    • H.B. Hunt III, D.J. Rosenkrantz, and T.G. Szymanski On the equivalence, containment, and covering problems for the regular and context-free languages J. Comput. System Sci. 12 1976 222 268
    • (1976) J. Comput. System Sci. , vol.12 , pp. 222-268
    • Hunt Iii, H.B.1    Rosenkrantz, D.J.2    Szymanski, T.G.3
  • 50
    • 67649996359 scopus 로고
    • Complexity of Closeness Sparseness and Segment Equivalence for Context-free and Regular Languages
    • Teubner, Informatik Festschrift zum 60
    • D.T. Huynh Complexity of Closeness Sparseness and Segment Equivalence for Context-free and Regular Languages Informatik Festschrift zum 60 Geburtstag von Günter Hotz 1992 Teubner pp. 235-251
    • (1992) Geburtstag von Günter Hotz
    • Huynh, D.T.1
  • 51
    • 85034748478 scopus 로고
    • On sparseness ambiguity and other decision problems for acceptors and transducers
    • Springer, Symposium on Theoretical Aspects of Computer Science (STACS 1986)
    • O.H. Ibarra, and B. Ravikumar On sparseness ambiguity and other decision problems for acceptors and transducers Symposium on Theoretical Aspects of Computer Science (STACS 1986) LNCS vol. 210 1986 Springer 171 179
    • (1986) LNCS , vol.210 , pp. 171-179
    • Ibarra, O.H.1    Ravikumar, B.2
  • 53
    • 0024091298 scopus 로고
    • Nondeterministic space is closed under complementation
    • N. Immerman Nondeterministic space is closed under complementation SIAM J. Comput. 17 1988 935 938
    • (1988) SIAM J. Comput. , vol.17 , pp. 935-938
    • Immerman, N.1
  • 55
    • 0013395658 scopus 로고
    • A note on the space complexity of some decision problems for finite automata
    • T. Jiang, and B. Ravikumar A note on the space complexity of some decision problems for finite automata Inform. Process. Lett. 40 1991 25 31
    • (1991) Inform. Process. Lett. , vol.40 , pp. 25-31
    • Jiang, T.1    Ravikumar, B.2
  • 56
    • 0027796975 scopus 로고
    • Minimal NFA problems are hard
    • T. Jiang, and B. Ravikumar Minimal NFA problems are hard SIAM J. Comput. 22 1993 1117 1141
    • (1993) SIAM J. Comput. , vol.22 , pp. 1117-1141
    • Jiang, T.1    Ravikumar, B.2
  • 57
    • 0016542395 scopus 로고
    • Space-bounded reducibility among combinatorial problems
    • N. Jones Space-bounded reducibility among combinatorial problems J. Comput. System Sci. 11 1975 68 85
    • (1975) J. Comput. System Sci. , vol.11 , pp. 68-85
    • Jones, N.1
  • 61
    • 0009977641 scopus 로고
    • Classes of languages and linear bounded automata
    • S.Y. Kuroda Classes of languages and linear bounded automata Inform. Control 7 1964 207 223
    • (1964) Inform. Control , vol.7 , pp. 207-223
    • Kuroda, S.Y.1
  • 62
    • 0002764923 scopus 로고
    • Über die Maximalordnung der Permutationen gegebenen Grades
    • E. Landau Über die Maximalordnung der Permutationen gegebenen Grades Archiv der Math. und Phys. 3 1903 92 103
    • (1903) Archiv der Math. und Phys. , vol.3 , pp. 92-103
    • Landau, E.1
  • 64
    • 84869181359 scopus 로고
    • The emptiness problem for intersections of regular languages
    • Springer, Mathematical Foundations of Computer Science (MFCS 1992)
    • K.J. Lange, and P. Rossmanith The emptiness problem for intersections of regular languages Mathematical Foundations of Computer Science (MFCS 1992) LNCS vol. 629 1992 Springer 346 354
    • (1992) LNCS , vol.629 , pp. 346-354
    • Lange, K.J.1    Rossmanith, P.2
  • 65
    • 0008200158 scopus 로고
    • Succinct representation of regular languages by Boolean automata
    • E. Leiss Succinct representation of regular languages by Boolean automata Theoret. Comput. Sci. 13 1981 323 330
    • (1981) Theoret. Comput. Sci. , vol.13 , pp. 323-330
    • Leiss, E.1
  • 66
    • 0022065091 scopus 로고
    • Succinct representation of regular languages by Boolean automata. II
    • DOI 10.1016/0304-3975(85)90215-4
    • E. Leiss Succinct representation of regular languages by Boolean automata. II Theoret. Comput. Sci. 38 1985 133 136 (Pubitemid 15584047)
    • (1985) Theoretical Computer Science , vol.38 , Issue.1 , pp. 133-136
    • Leiss Ernst1
  • 67
    • 6344292220 scopus 로고    scopus 로고
    • Minimizing finite automata is computationally hard
    • A. Malcher Minimizing finite automata is computationally hard Theoret. Comput. Sci. 327 2004 375 390
    • (2004) Theoret. Comput. Sci. , vol.327 , pp. 375-390
    • Malcher, A.1
  • 70
    • 0035704538 scopus 로고    scopus 로고
    • Optimal simulations between unary automata
    • DOI 10.1137/S009753979935431X, PII S009753979935431X
    • C. Mereghetti, and G. Pighizzini Optimal simulations between unary automata SIAM J. Comput. 30 2001 1976 1992 (Pubitemid 34125445)
    • (2001) SIAM Journal on Computing , vol.30 , Issue.6 , pp. 1976-1992
    • Mereghetti, C.1    Pighizzini, G.2
  • 72
    • 84985359842 scopus 로고
    • The equivalence problem for regular expressions with squaring requires exponential time
    • IEEE Press
    • A.R. Meyer, and L.J. Stockmeyer The equivalence problem for regular expressions with squaring requires exponential time Symposium on Switching and Automata Theory (SWAT 1972) 1972 IEEE Press 125 129
    • (1972) Symposium on Switching and Automata Theory (SWAT 1972) , pp. 125-129
    • Meyer, A.R.1    Stockmeyer, L.J.2
  • 73
    • 33750175613 scopus 로고
    • On the LBA problem
    • Springer, Fundamentals on Computation Theory (FCT 1981)
    • B. Monien On the LBA problem Fundamentals on Computation Theory (FCT 1981) LNCS vol. 117 1981 Springer 265 280
    • (1981) LNCS , vol.117 , pp. 265-280
    • Monien, B.1
  • 74
    • 0015145078 scopus 로고
    • On the bounds for state-set size in the proofs of equivalence between deterministic, nondeterministic, and two-way finite automata
    • F.R. Moore On the bounds for state-set size in the proofs of equivalence between deterministic, nondeterministic, and two-way finite automata IEEE Trans. Comput. 20 1971 1211 1214
    • (1971) IEEE Trans. Comput. , vol.20 , pp. 1211-1214
    • Moore, F.R.1
  • 75
    • 0000973916 scopus 로고
    • Finite automata and their decision problems
    • M.O. Rabin, and D. Scott Finite automata and their decision problems IBM J. Res. Dev. 3 1959 114 125
    • (1959) IBM J. Res. Dev. , vol.3 , pp. 114-125
    • Rabin, M.O.1    Scott, D.2
  • 78
    • 0000305750 scopus 로고
    • On finite monoids having only trivial subgroups
    • M.P. Schützenberger On finite monoids having only trivial subgroups Inform. Control 8 1965 190 194
    • (1965) Inform. Control , vol.8 , pp. 190-194
    • Schützenberger, M.P.1
  • 79
    • 0001751293 scopus 로고
    • Lower bounds on the size of sweeping automata
    • M. Sipser Lower bounds on the size of sweeping automata J. Comput. System Sci. 21 1980 195 202
    • (1980) J. Comput. System Sci. , vol.21 , pp. 195-202
    • Sipser, M.1
  • 80
    • 0022104603 scopus 로고
    • On the equivalence and containment problems for unambiguous regular expressions, regular grammars, and finite automata
    • R.E. Stearns, and H.B. Hunt III On the equivalence and containment problems for unambiguous regular expressions, regular grammars, and finite automata SIAM J. Comput. 14 1985 598 611 (Pubitemid 16460999)
    • (1985) SIAM Journal on Computing , vol.14 , Issue.3 , pp. 598-611
    • Stearns, R.E.1    Hunt III, H.B.2
  • 81
    • 0022116396 scopus 로고
    • Complexity of some problems from the theory of automata
    • J. Stern Complexity of some problems from the theory of automata Inform. Control 66 1985 163 176 (Pubitemid 16490700)
    • (1985) Information and control , vol.66 , Issue.3 , pp. 163-176
    • Stern Jacques1
  • 84
    • 0024112189 scopus 로고
    • The method of forced enumeration for nondeterministic automata
    • R. Szelepcsényi The method of forced enumeration for nondeterministic automata Acta Inform. 26 1988 279 284
    • (1988) Acta Inform. , vol.26 , pp. 279-284
    • Szelepcsényi, R.1
  • 85
    • 0001631788 scopus 로고
    • Classification of finite monoids: The language approach
    • D. Thérien Classification of finite monoids: the language approach Theoret. Comput. Sci. 14 1981 195 208
    • (1981) Theoret. Comput. Sci. , vol.14 , pp. 195-208
    • Thérien, D.1
  • 86
    • 49249151236 scopus 로고
    • The complexity of computing the permanent
    • L.G. Valiant The complexity of computing the permanent Theoret. Comput. Sci. 8 2 1979 189 201
    • (1979) Theoret. Comput. Sci. , vol.8 , Issue.2 , pp. 189-201
    • Valiant, L.G.1
  • 87
    • 11844290878 scopus 로고    scopus 로고
    • State complexity of regular languages
    • S. Yu State complexity of regular languages J. Autom. Lang. Comb. 6 2001 221 234
    • (2001) J. Autom. Lang. Comb. , vol.6 , pp. 221-234
    • Yu, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.