Abstract
We investigate normed commutative context-free processes (Basic Parallel Processes). We show that branching bisimilarity admits the bounded response property: in the Bisimulation Game, Duplicator always has a response leading to a process of size linearly bounded with respect to the Spoiler's process. The linear bound is effective, which leads to decidability of branching bisimilarity. For weak bisimilarity, we are able merely to show existence of some linear bound, which is not sufficient for decidability. We conjecture however that the same effective bound holds for weak bisimilarity as well. We suppose that further elaboration of novel techniques developed in this paper may be sufficient to demonstrate decidability.
Highlights
We investigate the class of commutative context-free processes, known under name Basic Parallel Processes (BPP) [1]
The right-hand side is a multiset rather than a sequence. Over this class of graphs, we focus on bisimulation equivalence as the primary type of semantic equality of processes
Less is known about weak bisimulation equivalence, that abstracts from the silent ε-transitions: we only know that it is semi-decidable [4] and that it is decidable in polynomial space over a very restricted class of totally normed processes [5]
Summary
Bisimulation equivalence (bisimilarity) is a fundamental notion of equivalence of processes, with many natural connections to logic, games and verification [12, 15]. We investigate the class of commutative context-free processes, known under name Basic Parallel Processes (BPP) [1]. Less is known about weak bisimulation equivalence, that abstracts from the silent ε-transitions: we only know that it is semi-decidable [4] and that it is decidable in polynomial space over a very restricted class of totally normed processes [5]. The only non-trivial decidability result known for weak bisimulation equivalence is proved in [16], it applies to a very restricted subclass.. One of the main obstacles in proving decidability of weak (or branching) bisimulation equivalence is that Duplicator may do arbitrarily many silent transitions in a single move, and the size of the resulting process is hard to bound. This paper is the full and improved version of the extended abstract [3]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
