Bisimilarity is not finitely based over BPA with interrupt (original) (raw)

Deciding Bisimilarity between BPA and BPP Processes

Lecture Notes in Computer Science, 2003

We identify a necessary condition for when a given BPP process can be expressed as a BPA process. We provide an effective procedure for testing if this condition holds of a given BPP, and in the positive case we provide an effective construction for a particular form of one-counter automaton which is bisimilar to the given BPP. This in turn provides the mechanism to decide bisimilarity between a given BPP process and a given BPA process.

On the existence of a finite base for complete trace equivalence over BPA with interrupt

We study Basic Process Algebra with interrupt modulo complete trace equivalence. We show that, unlike in the setting of the more demanding bisimilarity, a ground complete finite axiomatization exists. We explicitly give such an axiomatization, and extend it to a finite complete one in the special case when a single action is present. * The work of the authors has been partially supported by the project "The Equational Logic of Parallel Processes" (nr. 060013021) of The Icelandic Research Fund. 1 all immediate, given the many examples where a finite complete axiomatization does not exist.

Refining Undecidability Border of Weak Bisimilarity. (fullversion of INFINITY 2005 paper)

2005

Weak bisimilarity is one of the most studied behavioural equivalences. This equivalence is undecidable for pushdown processes (PDA), process algebras (PA), and multiset automata (MSA, also known as parallel pushdown processes, PPDA). Its decidability is an open question basic process algebras} (BPA) and basic parallel processes (BPP). We move the undecidability border towards these classes by showing that the equivalence remains undecidable for weakly extended versions of BPA and BPP.

Refining the Undecidability Border of Weak Bisimilarity

Electronic Notes in Theoretical Computer Science, 2006

Weak bisimilarity is one of the most studied behavioural equivalences. This equivalence is undecidable for pushdown processes (PDA), process algebras (PA), and multiset automata (MSA, also known as parallel pushdown processes, PPDA). Its decidability is an open question for basic process algebras (BPA) and basic parallel processes (BPP). We move the undecidability border towards these classes by showing that the equivalence remains undecidable for weakly extended versions of BPA and BPP. In fact, we show that the weak bisimulation equivalence problem is undecidable even for normed subclasses of BPA and BPP extended with a finite constraint system.

Bisimilarity of processes with finite-state systems

Electronic Notes in Theoretical Computer Science, 1997

We describe a general method for deciding bisimilarity for pairs of processes where one process has finitely many states. We apply this method to pushdown processes and to PA processes. We also demonstrate that the mentioned problem is undecidable for 'state-extended' PA processes.

Bisimulation indexes and their applications

2002

Bisimulation expresses the equivalence of processes whose external actions are identical. Sometimes we may meet two processes which are not exactly bisimilar but more or less bisimilar in the sense that whenever a process makes an action the other can make an action di erent from but very similar to the action performed by the ÿrst one. To describe this kind of looser bisimulations we propose the concept of bisimulation index in a labelled transition system and give its various properties, especially those properties related to the operations of transition systems. Furthermore, we establish a modal logical characterization of bisimulation indexes. This characterization is a generalization of Hennessy-Milner logic. We study strong and weak bisimulation indexes in the basic asynchronous process calculus, and some of their fundamental properties are derived. Bisimulation indexes are not substitutive under composition. To overcome this defect we introduce an approximate communication rule to replace the original rule in process calculus. This enables us to recover some useful properties of composition with respect to bisimulation indexes. Finally, we present three examples in timed CCS and real time ACP to demonstrate the usage of bisimulation indexes in the analysis of real time systems. These examples show that bisimulation indexes are suitable formal tools for describing approximate implementations of real time systems.