This chapter addresses the question how to verify distributed and communicating systems in an e#ective way from an explicit process algebraic standpoint. This means that all calculations are based on the axioms and principles of the process algebras.

We adapt the Coarsest Partition Refinement algorithm to its computation using the specific data structures of Binary Decision Diagrams. This allows to generate symbolically the set of equivalence classes of a finite automaton with respect to bisimulation, without constructing the automaton itself. These equivalence classes represent of course the (new) states of the canonical minimal automaton bisimilar to the early one. The method works from labeled synchronised vectors of automata as the distributed system description. We report on performances of Hoggar, a tool implementing our method. 1 Introduction Bisimulation is a central notion in the domain of verification of concurrent systems [18]. It was introduced as the major behavioural equivalence in the setting of process algebras [18, 2], but works at the interpretation level of labeled transition systems. Algorithmic properties of bisimulation in the finite state case have been widely studied [16, 20, 11], leading to a lar...

The analysis of programs by the exhaustive inspection of reachable states in a finite state graph is a well-understood procedure. It is straightforwardly applicable to many description languages and is actually implemented in several industrial tools. But one of the main limitations of today's verification tools is the size of the memory needed to exhaustively build the state graphs of the programs. For numerous properties, it is not necessary to explicitly build this graph and an exhaustive depth--first traversal is often sufficient. This leads to an on--line algorithms for computing Buchi acceptance (in the deterministic case) and behavioral equivalences: they are presented in detail. In order to avoid retraversing states, it is however important to store some of the already visited states in memory. To keep the memory size bounded (and avoid a performance falling down), visited states are randomly replaced. In most cases this depth--first traversal with replacement ca...

Recently, Milner and Moller have presented several decomposition results for processes. Inspired by these, we investigate decomposition techniques for the verification of parallel systems. In particular, we consider those of the form q j (I) where p i and q j are (finite) state systems. We provide a decomposition procedure for all p i and q j and give criteria that must be checked on the decomposed processes to see whether (I) does or does not hold. We analyse the complexity of our procedure and show that it is polynomial in n, m and the sizes of p i and q j if there is no communication. We also show that with communication the verification of (I) is co-NP hard, which makes it very unlikely that a polynomial complexity bound exists. But by applying our decomposition technique to Milner's cyclic scheduler we show that verification can become polynomial in space and time for practical examples, where standard techniques are exponential. Note: The authors are supported by the European Communities under ESPRIT Basic Research Action 3006 (CONCUR).

The analysis of programs by the exhaustive inspection of reachable states in a finite state graph is a well-understood procedure It is actually implemented in several industrial tools but one of their main limitations is the size of the memory needed to exhaustively build the state graphs of the programs. For numerous properties such as Buchi acceptance (in the deterministic case) and behavioral equivalence, it is not necessary to explicitly build this graph and an exhaustive depth--first traversal is often sufficient. In order to avoid retraversing states, it is however important to store in memory some of the already visited states and randomly replace them (to keep the memory size bounded and avoid a performance falling down) In most cases this depth--first traversal with replacement can push back significantly the limits of verification tools.

Abstract not found