On the verification problem of nonregular properties for nonregular processes

Investigate the verification problem of infinite-state processes w.r.t. nonregular properties, i.e. nondefinable by finite-state /spl omega/-automata. We consider processes in the algebra PA (Process Algebra) which provides sequential and parallel (merge) composition, nondeterministic choice and recursion. The algebra PA integrates and strictly subsumes the algebras BPA (Basic Process Algebra, i.e. context-free processes) and BPP (Basic Parallel Processes). On the other hand, we consider properties definable in a new temporal logic called CLTL (Constrained Linear-Time Logic) which is an extension of the linear-time temporal logic LTL with two kinds of constraints on traces: constraints on the numbers of occurrences of states expressed using Presburger formulas (occurrence constraints), and constraints on the order of appearance of states expressed using finite-state automata (pattern constraints). Pattern constraints allow to capture all the /spl omega/-regular properties whereas occurrence constraints allow to define nonregular properties. Then, we present (un)decidability results concerning the verification problem for the different classes of processes mentioned above and different fragments of CLTL.

[1]  Ahmed Bouajjani,et al.  Verifying infinite state processes with sequential and parallel composition , 1995, POPL '95.

[2]  Pierre Wolper.  Temporal Logic Can Be More Expressive , 1983, Inf. Control..

[3]  Fred Kröger,et al.  Temporal Logic of Programs , 1987, EATCS Monographs on Theoretical Computer Science.

[4]  Pierre Wolper,et al.  An Automata-Theoretic Approach to Automatic Program Verification (Preliminary Report) , 1986, LICS.

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

[6]  A. Prasad Sistla,et al.  Automatic verification of finite state concurrent system using temporal logic specifications: a practical approach , 1983, POPL '83.

[7]  Grzegorz Rozenberg,et al.  Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency , 1988, Lecture Notes in Computer Science.

[8]  John E. Hopcroft,et al.  On the Reachability Problem for 5-Dimensional Vector Addition Systems , 1976, Theor. Comput. Sci..

[9]  Moshe Y. Vardi.  A temporal fixpoint calculus , 1988, POPL '88.

[10]  Jan A. Bergstra,et al.  Decidability of bisimulation equivalence for process generating context-free languages , 1987, JACM.

[11]  Amir Pnueli,et al.  Propositional Dynamic Logic of Nonregular Programs , 1983, J. Comput. Syst. Sci..

[12]  Wolfgang Thomas,et al.  Star-Free Regular Sets of omega-Sequences , 1979, Inf. Control..

[13]  Amir Pnueli,et al.  The Glory of the Past , 1985, Logic of Programs.

[14]  Georg Peschke,et al.  The Theory of Ends , 1990 .

[15]  Chin-Laung Lei,et al.  Efficient Model Checking in Fragments of the Propositional Mu-Calculus (Extended Abstract) , 1986, LICS.

[16]  Parosh Aziz Abdulla,et al.  Verifying programs with unreliable channels , 1993, [1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science.

[17]  Javier Esparza,et al.  On the Decidability of Model Checking for Several µ-calculi and Petri Nets , 1994, CAAP.

[18]  Hans Hüttel,et al.  Decidability, Behavioural Equivalences and Infinite Transition Graphs , 1991 .

[19]  Søren Christensen,et al.  Decidability issues for infinite-state processes- a survey , 1993, Bull. EATCS.

[20]  Jan A. Bergstra,et al.  Process theory based on bisimulation semantics , 1988, REX Workshop.

[21]  Wolfgang Thomas,et al.  Automata on Infinite Objects , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[22]  Bernhard Steffen,et al.  Model Checking for Context-Free Processes , 1992, CONCUR.

[23]  Zohar Manna,et al.  A hierarchy of temporal properties (invited paper, 1989) , 1990, PODC '90.

[24]  Thomas A. Henzinger,et al.  A really temporal logic , 1989, 30th Annual Symposium on Foundations of Computer Science.

[25]  Søren Christensen.  Decidability and decomposition in process algebras , 1993 .

[26]  David E. Muller,et al.  The Theory of Ends, Pushdown Automata, and Second-Order Logic , 1985, Theor. Comput. Sci..

[27]  David Park,et al.  Concurrency and Automata on Infinite Sequences , 1981, Theoretical Computer Science.

[28]  Joseph Sifakis,et al.  Specification and verification of concurrent systems in CESAR , 1982, Symposium on Programming.

[29]  Ahmed Bouajjani,et al.  Verification of Nonregular Temporal Properties for Context-Free Processes , 1994, CONCUR.

[30]  Jan A. Bergstra,et al.  Decidability of Bisimulation Equivalence for Processes Generating Context-Free Languages , 1987, PARLE.