Stratified context unification is NP-complete

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4130 LNAI, Issue , 2006, Pages 82-96

  Levy, Jordi ^a   Schmidt Schauß, Manfred ^b   Villaret, Mateu ^c  

^a CSIC   (Spain)

^b GOETHE UNIVERSITY   (Germany)

^c IMA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTABILITY AND DECIDABILITY; CONSTRAINT THEORY; OPTIMIZATION; POLYNOMIALS; PROBLEM SOLVING;

CONTEXT UNIFICATION; PLANDOWSKI'S POLYNOMIAL ALGORITHM; SINGLETON TREE GRAMMARS;

COMPUTATIONAL COMPLEXITY;

EID: 33749580506     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11814771_8     Document Type: Conference Paper

References (32)

1. [And86] P. Andrews. An introduction t.o mathematical logic and type theory: to truth through proof. Academic Press. 1986.
2. [BLM05] G. Busatto, M. Lohrey, and S. Maneth. Efficient memory representation of XML documents. In Proc. DBPL 2005, LNCS 3774, pages 199-216, 2005.
3. +97] H. Comon, M. Dauchet, R. Gilleron, F. Jacquemard, D. Lugiez, S. Tison, and M. Tommasi. Tree automata techniques and applications. Available on: http://www.grappa.univ-lille3.fr/tata, 1997. release 1.10.2002.
4. [Dow01] G. Dowek. Higher-order unification and matching. In A. Robinson and A. Voronkov, editors, Handbook of Automated Reasoning, volume II, chapter 16, pages 1009-1062. Elsevier Science, 2001.
5. [EN00] K. Erk and J. Niehren. Parallelism constraints. In ATM-11, LNCS 1833, pages 110-126, 2000.
6. [Far91] W. M. Farmer. Simple second-order languages for wich unification is undecidable. Theoretical Computer Science, 87:173-214, 1991.
7. [Gol81] W. D. Goldfarb. The undecidability of the second-order unification problem. Theoretical Computer Science, 13:225-230, 1981.
8. [Hue75] G. Huet. A unification algorithm for typed λ-calculus. Theoretical Computer Science, 1:27-57, 1975.
9. [KNT98] A. Koller, J. Niehren, and R. Treinen. Dominance constraints: Algorithms and complexity. In 3rd LACL '98, LNCS 2014, pages 106-125, 1998.
10. [KP96] A. Kościelski and L. Pacholski. Complexity of Makanin's algorithm, Journal of the ACM, 43(4):670-684, 1996.
11. [Lev96] J. Levy, Linear second order unification. In RTA-7, LNCS 1103, pages 332-346, 1996.
12. [LNV05] J. Levy, J. Niehren, and M. Villaret. Well-nested context; unification. In CADE 2005, LNCS 3632, pages 149-163, 2005.
13. [LSSV04] J. Levy, M. Schmidt-Schauß, and M. Villaret. Monadic second-order unification is NP-complete. In RTA-15, LNCS 3091, pages 55-69, 2004.
14. [LSSV06] J. Levy, M. Schmidt-Schauß, and M. Villaret. Bounded second-order unification is NP-complete. to appear in Proc. RTA' 06, 2006.
15. [LV00] J. Levy and M. Veanes. On the undecidability of second-order unification. Information and Computation, 159:125-150, 2000.
16. [LV02] J. Levy and M. Villaret. Currying second-order unification problems. In RTA-13, LNCS 2378, pages 326-339, 2002.
17. [Mak77] G. S. Makanin. The problem of solvability of equations in a free semigroup. Math. USSR Sbornik, 32(2): 129-198, 1977.
18. [NK01] J. Niehren and A. Koller. Dominance constraints in context unification. In LACL'98, LNAI 2014, pages 199-218, 2001.
19. [NPR97a] J. Niehren, M. Pinkal, and P. Ruhrberg, On equality up-to constraints over finite trees, context unification, and one-step rewriting. In CADE-14, LNCS 1249, pages 34-48, 1997.
20. [NPR97b] J. Niehren, M. Pinkal, and P. Ruhrberg. A uniform approach to underspecification and parallelism. In 35th ACL'97, pages 410-417, Madrid, 1997.
21. [NTT00] J. Niehren, S. Tison, and R. Treinen, On rewrite constraints and context unification. Information Processing Letters, 74:35-40, 2000.
22. [Pau94] Lawrence C. Paulson. Isabelle. LNCS 828. Springer-Verlag, 1994.
23. [Pla94] W. Plandowski. Testing equivalence of morphisms in context-free languages. In J. van Leeuwen, editor, 2nd ESA '94, LNCS 855, pages 460-470, 1994.
24. [Pla95] W. Plandowski. The Complexity of the Morphism Equivalence Problem for Context-Free Languages. PhD thesis, Dept. of Mathematics, Informatics and Mechanics, Warsaw University, 1995.
25. [Pla04] W. Plandowski. Satisfiability of word equations with constants is in PSPACE. Journal of the ACM, 51(3):483-496, 2004.
26. [PS99] F. Pfenning and C. Schürmann, System description: Twelf - a meta-logical framework for deductive systems. In H. Ganzinger, editor, Proc. CADE-16, LNAI 1632, pages 202-206. Springer-Verlag, 1999.
27. [SAT06] 2006. http://www.satlive.org/.
28. [SS98] M. Schmidt-Schauß. A decision algorithm for distributive unification, TCS, 208:111-148, 1998.
29. [SS02] M. Schmidt-Schauæ. A decision algorithm for stratified context unification, Journal of Logic and Computation, 12(6):929-953, 2002.
30. [SS05] M. Schmidt-Schauæ, Polynomial equality testing for terms with shared substructures. Frank report 21, Institut für Informatik. FB Informatik und Mathematik. J. W. Goethe-Universität Frankfurt am Main, November 2005.
31. [SSS98] M. Schmidt-Schauæ and K. U. Schulz. On the exponent of periodicity of minimal solutions of context equations. In 9th RTA'98, LNCS 1379, pages 61-75, Tsukuba, Japan, 1998.
32. [SSS04] M. Schmidt-Schauæ and J. Stuber. On the complexity of linear and stratified context matching problems. Theory of Computing Systems, 37:717-740, 2004.