메뉴 건너뛰기




Volumn 4, Issue 2, 2012, Pages 241-299

Algorithmics on SLP-compressed strings: A survey

Author keywords

Algorithms for compressed strings; Compressed word problems; Computational complexity

Indexed keywords

COMPUTATIONAL COMPLEXITY; CONTEXT FREE GRAMMARS; FORMAL LANGUAGES; GROUP THEORY; PATTERN MATCHING;

EID: 84872769237     PISSN: 18671144     EISSN: 18696104     Source Type: Journal    
DOI: 10.1515/gcc-2012-0016     Document Type: Article
Times cited : (153)

References (144)
  • 2
    • 77954412402 scopus 로고    scopus 로고
    • A bisection algorithm for grammar-based compression of ordered trees
    • T. Akutsu, A bisection algorithm for grammar-based compression of ordered trees, Inf. Process. Lett. 110 (2010), no. 18-19, 815-820.
    • (2010) Inf. Process. Lett. , vol.110 , Issue.18-19 , pp. 815-820
    • Akutsu, T.1
  • 4
    • 84872897450 scopus 로고    scopus 로고
    • Technical Report DIKU Report 98/27, Department of Computer Science, University of Copenhagen
    • S. Alstrup, G. S. Brodal and T. Rauhe, Dynamic pattern matching, Technical Report DIKU Report 98/27, Department of Computer Science, University of Copenhagen, 1998.
    • (1998) Dynamic Pattern Matching
    • Alstrup, S.1    Brodal, G.S.2    Rauhe, T.3
  • 7
    • 0030129729 scopus 로고    scopus 로고
    • Let sleeping files lie: Pattern matching in Zcompressed files
    • A. Amir, G. Benson and M. Farach, Let sleeping files lie: Pattern matching in Zcompressed files, J. Comput. Syst. Sci. Int. 52 (1996), no. 2, 299-307.
    • (1996) J. Comput. Syst. Sci. Int. , vol.52 , Issue.2 , pp. 299-307
    • Amir, A.1    Benson, G.2    Farach, M.3
  • 9
    • 0024606026 scopus 로고
    • Bounded-width polynomial-size branching programs recognize exactly those languages in NC1
    • D. A. M. Barrington, Bounded-width polynomial-size branching programs recognize exactly those languages in NC1, J. Comput. Syst. Sci. Int. 38 (1989), 150-164.
    • (1989) J. Comput. Syst. Sci. Int. , vol.38 , pp. 150-164
    • Barrington, D.A.M.1
  • 11
  • 13
    • 79952139001 scopus 로고    scopus 로고
    • The inclusion problem of context-free languages: Some tractable cases
    • A. Bertoni, C. Choffrut and R. Radicioni, The inclusion problem of context-free languages: Some tractable cases, Int. J. Found. Comput. Sci. 22 (2011), no. 2, 289-299.
    • (2011) Int. J. Found. Comput. Sci. , vol.22 , Issue.2 , pp. 289-299
    • Bertoni, A.1    Choffrut, C.2    Radicioni, R.3
  • 14
    • 0031534568 scopus 로고    scopus 로고
    • Morse theory and finiteness properties of groups
    • M. Bestvina and N. Brady, Morse theory and finiteness properties of groups, Invent. Math. 129 (1997), no. 3, 445-470.
    • (1997) Invent. Math. , vol.129 , Issue.3 , pp. 445-470
    • Bestvina, M.1    Brady, N.2
  • 16
    • 0011994346 scopus 로고
    • The word problem
    • W. W. Boone, The word problem, Ann. of Math. (2) 70 (1959), 207-265.
    • (1959) Ann. of Math. , vol.2 , Issue.70 , pp. 207-265
    • Boone, W.W.1
  • 18
    • 43049155961 scopus 로고    scopus 로고
    • Efficient memory representation of XML document trees
    • G. Busatto, M. Lohrey and S. Maneth, Efficient memory representation of XML document trees, Information Systems 33 (2008), no. 4-5, 456-474.
    • (2008) Information Systems , vol.33 , Issue.4-5 , pp. 456-474
    • Busatto, G.1    Lohrey, M.2    Maneth, S.3
  • 19
    • 84972577723 scopus 로고
    • The word problem and power problem in 1-relator groups are primitive recursive
    • F. B. Cannonito and R. W. Gatterdam, The word problem and power problem in 1-relator groups are primitive recursive, Pacific J. Math. 61 (1975), no. 2, 351-359.
    • (1975) Pacific J. Math. , vol.61 , Issue.2 , pp. 351-359
    • Cannonito, F.B.1    Gatterdam, R.W.2
  • 26
    • 84856433861 scopus 로고    scopus 로고
    • Self-indexed Grammar-based compression
    • F. Claude and G. Navarro, Self-indexed grammar-based compression, Fundam. Inform. 111 (2011), no. 3, 313-337.
    • (2011) Fundam. Inform. , vol.111 , Issue.3 , pp. 313-337
    • Claude, F.1    Navarro, G.2
  • 28
    • 38249020685 scopus 로고
    • A uniform method for proving lower bounds on the computational complexity of logical theories
    • K. J. Compton and C. W. Henson, A uniform method for proving lower bounds on the computational complexity of logical theories, Ann. Pure Appl. Logic 48 (1990), 1-79.
    • (1990) Ann. Pure Appl. Logic , vol.48 , pp. 1-79
    • Compton, K.J.1    Henson, C.W.2
  • 29
    • 33750514881 scopus 로고    scopus 로고
    • Embeddings of graph braid and surface groups in right-angled artin groups and braid groups
    • J. Crisp and B.Wiest, Embeddings of graph braid and surface groups in right-angled artin groups and braid groups, Algebr. Geom. Topol. 4 (2004), 439-472.
    • (2004) Algebr. Geom. Topol. , vol.4 , pp. 439-472
    • Crisp, J.1    Wiest, B.2
  • 30
    • 0942266549 scopus 로고    scopus 로고
    • A subquadratic sequence alignment algorithm for unrestricted scoring matrices
    • M. Crochemore, G. M. Landau and M. Ziv-Ukelson, A subquadratic sequence alignment algorithm for unrestricted scoring matrices, SIAM J. Comput. 32 (2003), no. 6, 1654-1673.
    • (2003) SIAM J. Comput. , vol.32 , Issue.6 , pp. 1654-1673
    • Crochemore, M.1    Landau, G.M.2    Ziv-Ukelson, M.3
  • 31
    • 0000376243 scopus 로고
    • Die toplogie des dreidimensionalen raumes
    • M. Dehn, Über die Toplogie des dreidimensionalen Raumes, Math. Ann. 69 (1910), 137-168.
    • (1910) Math. Ann. , vol.69 , pp. 137-168
    • Dehn Über, M.1
  • 32
    • 4344714195 scopus 로고    scopus 로고
    • Makanin's algorithm
    • Cambridge University Press
    • V. Diekert, Makanin's algorithm, in: Algebraic Combinatorics on Words, Cambridge University Press (2001), 342-390.
    • (2001) Algebraic Combinatorics on Words , pp. 342-390
    • Diekert, V.1
  • 34
    • 0023842661 scopus 로고
    • Input-driven languages are in log n depth
    • P. W. Dymond, Input-driven languages are in log n depth, Inform. Process. Lett. 26 (1988), no. 5, 247-250.
    • (1988) Inform. Process. Lett. , vol.26 , Issue.5 , pp. 247-250
    • Dymond, P.W.1
  • 37
    • 0000573761 scopus 로고    scopus 로고
    • String matching in Lempel-Ziv compressed strings
    • M. Farach and M. Thorup, String matching in Lempel-Ziv compressed strings, Algorithmica 20 (1998), no. 4, 388-404.
    • (1998) Algorithmica , vol.20 , Issue.4 , pp. 388-404
    • Farach, M.1    Thorup, M.2
  • 38
    • 84966258522 scopus 로고
    • Uniqueness theorems for periodic functions
    • N. J. Fine and H. S. Wilf, Uniqueness theorems for periodic functions, Proc. Amer. Math. Soc. 16 (1965), 109-114.
    • (1965) Proc. Amer. Math. Soc. , vol.16 , pp. 109-114
    • Fine, N.J.1    Wilf, H.S.2
  • 40
    • 80051938966 scopus 로고    scopus 로고
    • Unification and matching on compressed terms
    • article number 26
    • A. Gascón, G. Godoy and M. Schmidt-Schauß, Unification and matching on compressed terms, ACM Trans. Comput. Log. 12 (2011), no. 4, article number 26.
    • (2011) ACM Trans. Comput. Log. , vol.12 , Issue.4
    • Gascón, A.1    Godoy, G.2    Schmidt-Schauß, M.3
  • 45
    • 33846842337 scopus 로고    scopus 로고
    • The geometry and topology of reconfiguration
    • R. Ghrist and V. Peterson, The geometry and topology of reconfiguration, Adv. in Appl. Math. 38 (2007), no. 3, 302-323.
    • (2007) Adv. In Appl. Math. , vol.38 , Issue.3 , pp. 302-323
    • Ghrist, R.1    Peterson, V.2
  • 47
    • 0019703239 scopus 로고
    • Productions in context-free grammars
    • L. M. Goldschlager, "-productions in context-free grammars, Acta Inform. 16 (1981), 303-308.
    • (1981) Acta Inform. , vol.16 , pp. 303-308
    • Goldschlager, L.M.1
  • 50
    • 0000348710 scopus 로고
    • The hardest context-free language
    • S. Greibach, The hardest context-free language, SIAM J. Comput. 2 (1973), no. 4, 304-310.
    • (1973) SIAM J. Comput. , vol.2 , Issue.4 , pp. 304-310
    • Greibach, S.1
  • 55
    • 77952959019 scopus 로고    scopus 로고
    • Coxeter groups are virtually special
    • F. Haglund and D. T. Wise, Coxeter groups are virtually special, Adv. Math. 224 (2010), no. 5, 1890-1903.
    • (2010) Adv. Math. , vol.224 , Issue.5 , pp. 1890-1903
    • Haglund, F.1    Wise, D.T.2
  • 56
    • 79958026716 scopus 로고    scopus 로고
    • Compressed word problems in HNN-extensions and amalgamated products
    • N. Haubold and M. Lohrey, Compressed word problems in HNN-extensions and amalgamated products, Theory Comput. Syst. 49 (2011), no. 2, 283-305.
    • (2011) Theory Comput. Syst. , vol.49 , Issue.2 , pp. 283-305
    • Haubold, N.1    Lohrey, M.2
  • 57
    • 78049242476 scopus 로고    scopus 로고
    • Compressed conjugacy and the word problem for outer automorphism groups of graph groups
    • Springer. Long version in Internat. J. Algebra Comput., to appear
    • N. Haubold, M. Lohrey and C. Mathissen, Compressed conjugacy and the word problem for outer automorphism groups of graph groups, in: Proceedings of Developments in Language Theory (DLT 2010), Lecture Notes in Comput. Sci. 6224, Springer (2010), 218-230. Long version in Internat. J. Algebra Comput., to appear.
    • (2010) Proceedings of Developments in Language Theory (DLT 2010), Lecture Notes in Comput. Sci. , vol.6224 , pp. 218-230
    • Haubold, N.1    Lohrey, M.2    Mathissen, C.3
  • 60
    • 0030145876 scopus 로고    scopus 로고
    • A polynomial algorithm for deciding bisimilarity of normed context-free processes
    • Y. Hirshfeld, M. Jerrum and F. Moller, A polynomial algorithm for deciding bisimilarity of normed context-free processes, Theoret. Comput. Sci. 158 (1996), no. 1-2, 143-159.
    • (1996) Theoret. Comput. Sci. , vol.158 , Issue.1-2 , pp. 143-159
    • Hirshfeld, Y.1    Jerrum, M.2    Moller, F.3
  • 62
    • 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. Syst. Sci. 12 (1976), no. 2, 222-268.
    • (1976) J. Comput. Syst. Sci. , vol.12 , Issue.2 , pp. 222-268
    • Hunt III, H.B.1    Rosenkrantz, D.J.2    Szymanski, T.G.3
  • 63
    • 84976819141 scopus 로고
    • Probabilistic algorithms for deciding equivalence of straight-line programs
    • O. H. Ibarra and S. Moran, Probabilistic algorithms for deciding equivalence of straight-line programs, J. ACM 30 (1983), no. 1, 217-228.
    • (1983) J. ACM , vol.30 , Issue.1 , pp. 217-228
    • Ibarra, O.H.1    Moran, S.2
  • 68
    • 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), no. 1, 25-31.
    • (1991) Inform. Process. Lett. , vol.40 , Issue.1 , pp. 25-31
    • Jiang, T.1    Ravikumar, B.2
  • 69
    • 0023826531 scopus 로고
    • Greatest common divisors of polynomials given by straight-line programs
    • E. Kaltofen, Greatest common divisors of polynomials given by straight-line programs, J. ACM 35 (1988), no. 1, 231-264.
    • (1988) J. ACM , vol.35 , Issue.1 , pp. 231-264
    • Kaltofen, E.1
  • 70
    • 0037673298 scopus 로고    scopus 로고
    • Generic-case complexity, decision problems in group theory, and random walks
    • I. Kapovich, A. Miasnikov, P. Schupp and V. Shpilrain, Generic-case complexity, decision problems in group theory, and random walks, J. Algebra 264 (2003), no. 2, 665-694.
    • (2003) J. Algebra , vol.264 , Issue.2 , pp. 665-694
    • Kapovich, I.1    Miasnikov, A.2    Schupp, P.3    Shpilrain, V.4
  • 71
    • 0024627791 scopus 로고
    • The iterated mod problem
    • H. J. Karloff and W. L. Ruzzo, The iterated mod problem, Inform. and Comput. 80 (1989), no. 3, 193-204.
    • (1989) Inform. and Comput. , vol.80 , Issue.3 , pp. 193-204
    • Karloff, H.J.1    Ruzzo, W.L.2
  • 79
    • 55249085853 scopus 로고    scopus 로고
    • The complexity of monadic secondorder unification
    • J. Levy, M. Schmidt-Schauß and M. Villaret, The complexity of monadic secondorder unification, SIAM J. Comput. 38 (2008), no. 3, 1113-1140.
    • (2008) SIAM J. Comput. , vol.38 , Issue.3 , pp. 1113-1140
    • Levy, J.1    Schmidt-Schauß, M.2    Villaret, M.3
  • 82
    • 67349186481 scopus 로고    scopus 로고
    • Speeding up HMM decoding and training by exploiting sequence repetitions
    • Y. Lifshits, S. Mozes, O.Weimann and M. Ziv-Ukelson, Speeding up HMM decoding and training by exploiting sequence repetitions, Algorithmica 54 (2009), no. 3, 379-399.
    • (2009) Algorithmica , vol.54 , Issue.3 , pp. 379-399
    • Lifshits, Y.1    Mozes, S.2    Weimann, O.3    Ziv-Ukelson, M.4
  • 83
    • 84976851566 scopus 로고
    • Word problems solvable in logspace
    • R. J. Lipton and Y. Zalcstein, Word problems solvable in logspace, J. ACM 24 (1977), no. 3, 522-526.
    • (1977) J. ACM , vol.24 , Issue.3 , pp. 522-526
    • Lipton, R.J.1    Zalcstein, Y.2
  • 84
    • 33749260063 scopus 로고    scopus 로고
    • Word problems and membership problems on compressed words
    • M. Lohrey,Word problems and membership problems on compressed words, SIAM J. Comput. 35 (2006), no. 5, 1210-1240.
    • (2006) SIAM J. Comput. , vol.35 , Issue.5 , pp. 1210-1240
    • Lohrey, M.1
  • 85
    • 77957801579 scopus 로고    scopus 로고
    • Compressed membership problems for regular expressions and hierarchical automata
    • M. Lohrey, Compressed membership problems for regular expressions and hierarchical automata, Internat. J. Found. Comput. Sci. 21 (2010), no. 5, 817-841.
    • (2010) Internat. J. Found. Comput. Sci. , vol.21 , Issue.5 , pp. 817-841
    • Lohrey, M.1
  • 87
    • 79952581732 scopus 로고    scopus 로고
    • Leaf languages and string compression
    • M. Lohrey, Leaf languages and string compression, Inform. and Comput. 209 (2011), no. 6, 951-965.
    • (2011) Inform. and Comput. , vol.209 , Issue.6 , pp. 951-965
    • Lohrey, M.1
  • 88
    • 84855987726 scopus 로고    scopus 로고
    • Model-checking hierarchical structures
    • M. Lohrey, Model-checking hierarchical structures, J. Comput. Syst. Sci. Int. 78 (2012), no. 2, 461-490.
    • (2012) J. Comput. Syst. Sci. Int. , vol.78 , Issue.2 , pp. 461-490
    • Lohrey, M.1
  • 89
    • 33749266917 scopus 로고    scopus 로고
    • The complexity of tree automata and XPath on grammarcompressed trees
    • M. Lohrey and S. Maneth, The complexity of tree automata and XPath on grammarcompressed trees, Theoret. Comput. Sci. 363 (2006), no. 2, 196-210.
    • (2006) Theoret. Comput. Sci. , vol.363 , Issue.2 , pp. 196-210
    • Lohrey, M.1    Maneth, S.2
  • 91
    • 84861605753 scopus 로고    scopus 로고
    • Parameter reduction and automata evaluation for grammar-compressed trees
    • M. Lohrey, S. Maneth and M. Schmidt-Schauß, Parameter reduction and automata evaluation for grammar-compressed trees, J. Comput. System Sci. 78 (2012), no. 5, 1651-1669.
    • (2012) J. Comput. System Sci. , vol.78 , Issue.5 , pp. 1651-1669
    • Lohrey, M.1    Maneth, S.2    Schmidt-Schauß, M.3
  • 96
    • 77953771005 scopus 로고    scopus 로고
    • Compressed words and automorphisms in fully residually free groups internat
    • J. Macdonald, Compressed words and automorphisms in fully residually free groups, Internat. J. Algebra Comput. 20 (2010), no. 3, 343-355.
    • (2010) J. Algebra Comput. , vol.20 , Issue.3 , pp. 343-355
    • Macdonald, J.1
  • 97
    • 0000240765 scopus 로고
    • The problem of solvability of equations in a free semigroup (in Russian
    • translation in Math. USSR Sbornik 32 (1977), 129-198
    • G. S. Makanin, The problem of solvability of equations in a free semigroup (in Russian), Math. Sbornik 103 (1977), 147-236; translation in Math. USSR Sbornik 32 (1977), 129-198.
    • (1977) Math. Sbornik , vol.103 , pp. 147-236
    • Makanin, G.S.1
  • 99
    • 1442356676 scopus 로고    scopus 로고
    • A PTIME-complete matching problem for SLPcompressed words
    • N. Markey and P. Schnoebelen, A PTIME-complete matching problem for SLPcompressed words, Inform. Process. Lett. 90 (2004), no. 1, 3-6.
    • (2004) Inform. Process. Lett. , vol.90 , Issue.1 , pp. 3-6
    • Markey, N.1    Schnoebelen, P.2
  • 102
    • 59049103692 scopus 로고    scopus 로고
    • Efficient algorithms to compute compressed longest common substrings and compressed palindromes
    • W. Matsubara, S. Inenaga, A. Ishino, A. Shinohara, T. Nakamura and K. Hashimoto, Efficient algorithms to compute compressed longest common substrings and compressed palindromes, Theoret. Comput. Sci. 410 (2009), no. 8-10, 900-913.
    • (2009) Theoret. Comput. Sci. , vol.410 , Issue.8-10 , pp. 900-913
    • Matsubara, W.1    Inenaga, S.2    Ishino, A.3    Shinohara, A.4    Nakamura, T.5    Hashimoto, K.6
  • 103
    • 0001553469 scopus 로고
    • The complexity of word problems-This time with interleaving
    • A. J. Mayer and L. J. Stockmeyer, The complexity of word problems-This time with interleaving, Inform. and Comput. 115 (1994), no. 2, 293-311.
    • (1994) Inform. and Comput. , vol.115 , Issue.2 , pp. 293-311
    • Mayer, A.J.1    Stockmeyer, L.J.2
  • 104
    • 0037801365 scopus 로고    scopus 로고
    • Maintaining dynamic sequences under equality tests in polylogarithmic time
    • K. Mehlhorn, R. Sundar and C. Uhrig, Maintaining dynamic sequences under equality tests in polylogarithmic time, Algorithmica 17 (1997), no. 2, 183-198.
    • (1997) Algorithmica , vol.17 , Issue.2 , pp. 183-198
    • Mehlhorn, K.1    Sundar, R.2    Uhrig, C.3
  • 106
    • 84865722341 scopus 로고    scopus 로고
    • Power circuits, exponential algebra, and time complexity, Internat
    • A. G. Myasnikov, A. Ushakov and D.W.Won, Power circuits, exponential algebra, and time complexity, Internat. J. Algebra Comput. 22 (2012), no. 6, 1-51.
    • (2012) J. Algebra Comput. , vol.22 , Issue.6 , pp. 1-51
    • Myasnikov, A.G.1    Ushakov, A.2    Won, D.W.3
  • 107
    • 3042662535 scopus 로고    scopus 로고
    • The language intersection problem for non-recursive context-free grammars
    • M.-J. Nederhof and G. Satta, The language intersection problem for non-recursive context-free grammars, Inform. and Comput. 192 (2004), no. 2, 172-184.
    • (2004) Inform. and Comput. , vol.192 , Issue.2 , pp. 172-184
    • Nederhof, M.-J.1    Satta, G.2
  • 108
    • 2642531180 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, Amer. Math. Soc. Transl. Ser. 2 9 (1958), 1-122.
    • (1958) Amer. Math. Soc. Transl. Ser. , vol.2 , Issue.9 , pp. 1-122
    • Novikov, P.S.1
  • 112
    • 4243105086 scopus 로고    scopus 로고
    • Satisfiability of word equations with constants is in PSPACE
    • W. Plandowski, Satisfiability of word equations with constants is in PSPACE, J. ACM 51 (2004), no. 3, 483-496.
    • (2004) J. ACM , vol.51 , Issue.3 , pp. 483-496
    • Plandowski, W.1
  • 115
    • 84872951242 scopus 로고    scopus 로고
    • Grammatical compression: Compressed equivalence and other problems
    • R. Radicioni and A. Bertoni, Grammatical compression: Compressed equivalence and other problems, Discrete Math. Theor. Comput. Sci. 12 (2010), no. 4, 109-126.
    • (2010) Discrete Math. Theor. Comput. Sci. , vol.12 , Issue.4 , pp. 109-126
    • Radicioni, R.1    Bertoni, A.2
  • 118
    • 0038238644 scopus 로고    scopus 로고
    • Application of lempel-ziv factorization to the approximation of grammar-based compression
    • W. Rytter, Application of Lempel-Ziv factorization to the approximation of grammar-based compression, Theoret. Comput. Sci. 302 (2003), no. 1-3, 211-222.
    • (2003) Theoret. Comput. Sci. , vol.302 , Issue.1-3 , pp. 211-222
    • Rytter, W.1
  • 120
    • 18544376055 scopus 로고    scopus 로고
    • A fully linear-time approximation algorithm for grammar-based compression
    • H. Sakamoto, A fully linear-time approximation algorithm for grammar-based compression, J. Discrete Algorithms 3 (2005), no. 2-4, 416-430.
    • (2005) J. Discrete Algorithms , vol.3 , Issue.2-4 , pp. 416-430
    • Sakamoto, H.1
  • 124
    • 55349141807 scopus 로고    scopus 로고
    • Polynomial-time word problems
    • S. Schleimer, Polynomial-time word problems, Comment. Math. Helv. 83 (2008), no. 4, 741-765.
    • (2008) Comment. Math. Helv. , vol.83 , Issue.4 , pp. 741-765
    • Schleimer, S.1
  • 128
    • 84856593292 scopus 로고    scopus 로고
    • Fast equality test for straight-line compressed strings
    • M. Schmidt-Schauß and G. Schnitger, Fast equality test for straight-line compressed strings, Inf. Process. Lett. 112 (2012), no. 8-9, 341-345.
    • (2012) Inf. Process. Lett. , vol.112 , Issue.8-9 , pp. 341-345
    • Schmidt-Schauß, M.1    Schnitger, G.2
  • 131
    • 84976758731 scopus 로고
    • On the tape complexity of deterministic context-free languages
    • I. H. Sudborough, On the tape complexity of deterministic context-free languages, J. ACM 25 (1978), no. 3, 405-414.
    • (1978) J. ACM , vol.25 , Issue.3 , pp. 405-414
    • Sudborough, I.H.1
  • 132
    • 67349251202 scopus 로고    scopus 로고
    • Faster subsequence recognition in compressed strings
    • A. Tiskin, Faster subsequence recognition in compressed strings, J. Math. Sci. (N.Y.) 158 (2009), no. 5, 759-769.
    • (2009) J. Math. Sci. (N.Y. , vol.158 , Issue.5 , pp. 759-769
    • Tiskin, A.1
  • 134
    • 0026239342 scopus 로고
    • PP is as hard as the polynomial-time hierarchy
    • S. Toda, PP is as hard as the polynomial-time hierarchy, SIAM J. Comput. 20 (1991), no. 5, 865-877.
    • (1991) SIAM J. Comput. , vol.20 , Issue.5 , pp. 865-877
    • Toda, S.1
  • 137
    • 0026237246 scopus 로고
    • Properties that characterize LOGCFL
    • H. Venkateswaran, Properties that characterize LOGCFL, J. Comput. Syst. Sci. Int. 43 (1991), 380-404.
    • (1991) J. Comput. Syst. Sci. Int. , vol.43 , pp. 380-404
    • Venkateswaran, H.1
  • 138
    • 0022733806 scopus 로고
    • The complexity of combinatorial problems with succinct input representation
    • K. W. Wagner, The complexity of combinatorial problems with succinct input representation, Acta Inform. 23 (1986), no. 3, 325-356.
    • (1986) Acta Inform. , vol.23 , Issue.3 , pp. 325-356
    • Wagner, K.W.1
  • 140
    • 0000746072 scopus 로고
    • On the complexity of iterated shuffle
    • M. K. Warmuth and D. Haussler, On the complexity of iterated shuffle, J. Comput. Syst. Sci. Int. 28 (1984), no. 3, 345-358.
    • (1984) J. Comput. Syst. Sci. Int. , vol.28 , Issue.3 , pp. 345-358
    • Warmuth, M.K.1    Haussler, D.2
  • 141
    • 77953707659 scopus 로고    scopus 로고
    • Research announcement: The structure of groups with a quasiconvex hierarchy
    • D. T. Wise, Research announcement: The structure of groups with a quasiconvex hierarchy, Electron. Res. Announc.Math. Sci. 16 (2009), 44-55.
    • (2009) Electron. Res. Announc.Math. Sci. , vol.16 , pp. 44-55
    • Wise, D.T.1
  • 143
    • 0346395014 scopus 로고
    • On the evaluation of powers
    • A. C.-C. Yao, On the evaluation of powers, SIAM J. Comput. 5 (1976), no. 1, 100-103.
    • (1976) SIAM J. Comput. , vol.5 , Issue.1 , pp. 100-103
    • Yao, A.C.-C.1
  • 144
    • 0017493286 scopus 로고
    • A universal algorithm for sequential data compression
    • J. Ziv and A. Lempel, A universal algorithm for sequential data compression, IEEE Trans. Inf. Theory 23 (1977), no. 3, 337-343.
    • (1977) IEEE Trans. Inf. Theory , vol.23 , Issue.3 , pp. 337-343
    • Ziv, J.1    Lempel, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.