EXPTIME-completeness of thorough refinement on modal transition systems

Abstract Modal transition systems (MTS), a specification formalism introduced more than 20 years ago, has recently received a considerable attention in several different areas. Many of the fundamental questions related to MTSs have already been answered. However, the problem of the exact computational complexity of thorough refinement checking between two finite MTSs remained unsolved. We settle down this question by showing EXPTIME-completeness of thorough refinement checking on finite MTSs. The upper-bound result relies on a novel algorithm running in single exponential time providing a direct goal-oriented way to decide thorough refinement. If the right-hand side MTS is moreover deterministic, or has a fixed size, the running time of the algorithm becomes polynomial. The lower-bound proof is achieved by reduction from the acceptance problem of alternating linear bounded automata and the problem remains EXPTIME-hard even if the left-hand side MTS is fixed and deterministic.

[1]  Robert E. Tarjan,et al.  Three Partition Refinement Algorithms , 1987, SIAM J. Comput..

[2]  Sebastián Uchitel,et al.  MTSA: Eclipse support for modal transition systems construction, analysis and elaboration , 2007, eclipse '07.

[3]  Marsha Chechik,et al.  Merging partial behavioural models , 2004, SIGSOFT '04/FSE-12.

[4]  Kim G. Larsen,et al.  Modal and mixed specifications: key decision problems and their complexities , 2010, Mathematical Structures in Computer Science.

[5]  Kim G. Larsen,et al.  On determinism in modal transition systems , 2009, Theor. Comput. Sci..

[6]  Radha Jagadeesan,et al.  Modal Transition Systems: A Foundation for Three-Valued Program Analysis , 2001, ESOP.

[7]  Roberto Passerone,et al.  Why Are Modalities Good for Interface Theories? , 2009, 2009 Ninth International Conference on Application of Concurrency to System Design.

[8]  José L. Balcázar,et al.  Deciding Bisimilarity is P-Complete , 1992, Formal Aspects Comput..

[9]  Harald Fecher,et al.  Comparing disjunctive modal transition systems with an one-selecting variant , 2008, J. Log. Algebraic Methods Program..

[10]  J. Gabarró,et al.  Deciding bisimilarity isP-complete , 1992, Formal Aspects of Computing.

[11]  Petr Jancar,et al.  Behavioural Equivalences on Finite-State Systems are PTIME-hard , 2005, Comput. Artif. Intell..

[12]  Thomas A. Henzinger,et al.  The Embedded Systems Design Challenge , 2006, FM.

[13]  Scott A. Smolka,et al.  CCS expressions, finite state processes, and three problems of equivalence , 1983, PODC '83.

[14]  Kim G. Larsen,et al.  Complexity of Decision Problems for Mixed and Modal Specifications , 2008, FoSSaCS.

[15]  Kim G. Larsen,et al.  On Modal Refinement and Consistency , 2007, CONCUR.

[16]  Flemming Nielson,et al.  Modal Abstractions of Concurrent Behaviour , 2008, SAS.

[17]  Radha Jagadeesan,et al.  Abstraction-Based Model Checking Using Modal Transition Systems , 2001, CONCUR.

[18]  Jean-Baptiste Raclet,et al.  Residual for Component Specifications , 2008, Electron. Notes Theor. Comput. Sci..

[19]  Kim G. Larsen,et al.  A modal process logic , 1988, [1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science.

[20]  Nathalie Bertrand,et al.  Refinement and Consistency of Timed Modal Specifications , 2009, LATA.

[21]  Orna Grumberg,et al.  Compositional verification and 3-valued abstractions join forces , 2010, Inf. Comput..

[22]  Sebastián Uchitel,et al.  MTSA: The Modal Transition System Analyser , 2008, 2008 23rd IEEE/ACM International Conference on Automated Software Engineering.

[23]  Thomas A. Henzinger,et al.  The Discipline of Embedded Systems Design , 2007, Computer.

[24]  Rolf Hennicker,et al.  On Weak Modal Compatibility, Refinement, and the MIO Workbench , 2010, TACAS.

[25]  Marsha Chechik,et al.  Mixed Transition Systems Revisited , 2008, VMCAI.

[26]  Kim G. Larsen,et al.  20 Years of Modal and Mixed Specifications , 2008, Bull. EATCS.

[27]  Michael Sipser,et al.  Introduction to the Theory of Computation , 1996, SIGA.