Deciding Bisimulation-Like Equivalences with Finite-State Processes (original) (raw)
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Decidability of bisimulation equivalences for parallel timer processes
Lecture Notes in Computer Science, 1993
In this paper an abstract model of parallel timer processes (PTPs), allowing specification of temporal quantitative constraints on the behaviour of real time systems, is introduced. The parallel timer processes are defined in a dense time domain and are able to model both concurrent (with delay intervals overlapping on the time axis) and infinite behaviour. Both the strong and weak (abstracted from internal actions) bisimulation equivalence problems for PTPs are proved decidable. It is proved also that, if one provides the PTP model additionally with memory cells for moving timer value information along the time axis, the bisimulation equivalence (and even the vertex teachability) problems become undecidable.
Information and Computation, 2010
Simulation preorder/equivalence and bisimulation equivalence are the most commonly used equivalences in concurrency theory. Their standard definitions are often called strong simulation/bisimulation, while weak simulation/bisimulation abstracts from internal τ-actions. We study the computational complexity of checking these strong and weak semantic preorders/equivalences between pushdown processes and finite-state processes. We present a complete picture of the computational complexity of these problems and also study fixed-parameter tractability in two important input parameters: x, the size of the finite control of the pushdown process, and y, the size of the finite-state process. All simulation problems are generally EXPTIME-complete and only become polynomial if both parameters x and y are fixed. Weak bisimulation equivalence is PSPACE-complete, but becomes polynomial if and only if parameter x is fixed. Strong bisimulation equivalence is PSPACE-complete, but becomes polynomial if either parameter x or y is fixed.
1995
We present a uniform approach for proving the polynomial time decidability of various simulation and equivalence relations for finite state processes. Our approach applies directly to a number of simulation relations and equivalences considered in the literature including strong bisimulation [Par81, Mil80, KS90], simulation equivalence [vG90, HT94], readysimulation equivalence [vG90, HT94], complete simulation equivalence [vG90], possibilities equivalence (also known as forward simulation) and backward simulation ...
Bisimulation equivalence is decidable for basic parallel processes
Lecture Notes in Computer Science, 1993
In a previous paper the authors proved the decidability of bisimulation equivalence over two subclasses of recurslve processes involving a parallel composition operator, namely the so-caUed norrned and live processes. In this paper, we extend this result to the whole class. The decidability proof permits us further to present a complete axiomatisation for this class of basic parallel processes. This result can be viewed as a proper extension of Miiner's complete axiomatisation of bisimulation equivalence on regular processes.
A general approach to comparing infinite-state systems with their finite-state specifications
Theoretical Computer Science, 2006
We introduce a generic family of behavioral relations for which the regular equivalence problem (i.e., comparing an arbitrary transition system to some finite-state specification) can be reduced to the model checking problem against simple modal formulae. As an application, we derive decidability of several regular equivalence problems for well-known families of infinite-state systems.
Decidability of bisimulation equivalence for process generating context-free languages
Journal of the ACM, 1993
A context-free grammar (CFG) in Greibach Normal Form coincides, in another notation, with a system of guarded recursion equations in Basic Process Algebra. Hence to each CFG a process can be assigned as solution, which has as its set of finite traces the context-free language (CFL) determined by that CFG. While the equality problem for CFL's is unsolvable, the equality problem for the processes determined by CFG's turns out to be solvable. Here equality on processes is given by a model of process graphs modulo bisimulation equivalence. The proof is given by displaying a periodic structure of the process graphs determined by CFG's. As a corollary of the periodicity a short proof of the solvability of the equivalence problem for simple context-free languages is given.
On decidability of LTL model checking for process rewrite systems
Acta Informatica, 2009
We establish a decidability boundary of the model checking problem for infinitestate systems defined by Process Rewrite Systems (PRS) or weakly extended Process Rewrite Systems (wPRS), and properties described by basic fragments of action-based Linear Temporal Logic (LTL) with both future and past operators. It is known that the problem for general LTL properties is decidable for Petri nets and for pushdown processes, while it is undecidable for PA processes. We show that the problem is decidable for wPRS if we consider properties defined by LTL formulae with only modalities strict eventually, strict always, and their past counterparts. Moreover, we show that the problem remains undecidable for PA processes even with respect to the LTL fragment with the only modality until or the fragment with modalities next and infinitely often. 2 L. Bozzelli et al.
IFIP International Federation for Information Processing, 2004
We propose a generic method for deciding semantic equivalences between pushdown automata and finite-state automata. The abstract part of the method is applicable to every process equivalence which is a right PDA congruence. Practical usability of the method is demonstrated on selected equivalences which are conceptual representatives of the whole spectrum. In particular, special attention is devoted to bisimulation-like equivalences (including weak, early, delay, branching, and probabilistic bisimilarity), and it is also shown how the method applies to simulation-like and trace-like equivalences. The generality does not lead to the loss of efficiency; the algorithms obtained by applying our method are essentially time-optimal and sometimes even polynomial. The list of particular results obtained by our method includes items which are first of their kind. Formal verification; Pushdown automata; Semantic equivalences; *On leave at the Institute for Formal Methods in Computer Science,