Model checking for process rewrite systems and a class of action-based regular properties

Laura Bozzelli
2006 Theoretical Computer Science  
We consider the model checking problem for Process Rewrite Systems (PRS), an infinite-state formalism (non Turing-powerful) which subsumes many common models such as Pushdown Processes and Petri Nets. PRS can be adopted as a formal model for programs with dynamic creation and synchronization of concurrent processes, and with recursive procedures. The model-checking problem of PRS against action-based linear temporal logic (ALTL) is undecidable. However, decidability for some interesting
more » ... of ALTL remains an open question. In this paper, we state decidability results concerning generalized acceptance properties about infinite derivations (infinite term rewriting) in PRS. As a consequence, we obtain decidability of the model-checking problem (restricted to infinite runs) of PRS against a meaningful fragment of ALTL. where is an ALTL propositional formula, a is an atomic action, and a , G, and U are the next, always, and until operators. 2 1 and 2 denote ALTL propositional formulae. 7 We assume that sequential composition is left-associative. So, when we write t 1 .t 2 , then t 2 is either a single variable or a parallel composition of process terms. 8 Note that we have not specified the label of the new rules, since it is not relevant. 9 Note that the number of new rules added in order to built M PAR , M SEQ , M K,K PAR , and M K,K PAR,∞ is exponential in n and polynomial in |Var( )|.
doi:10.1016/j.tcs.2006.05.003 fatcat:xutiox5dkzdrpf4yp7t6nhafie