Domain-specific regular acceleration

Abstract

Abstract. The regular model-checking approach is a set of techniques aimed at exploring symbolically infinite state spaces. These techniques proceed by representing sets of configurations of the system under analysis by regular languages, and the transition relation between these configurations by a transformation over such languages. The set of reachable configurations can then be computed by repeatedly applying the transition relation, starting from a representation of the initial set of configurations, until a fixed point is reached.In order for this computation to terminate, it is generally needed to introduce so-called acceleration operators, the purpose of which is to explore in one computation step infinitely many paths in the transition graph of the system. A simple form of acceleration operator is one that is associated to a cycle in the transition graph, computing the set of states that can be obtained by following this cycle arbitrarily many times.The computation of acceleration operators is strongly dependent on the type of the data values that are manipulated by the system, and on the symbolic representation chosen for handling sets of such values. In this survey, we describe acceleration operators suited for the regular state-space exploration of systems relying on FIFO communication channels, as well as those based on integer and real variables.

Regular model checking

“…Furthermore, it shows how to extend the techniques to the case of trees. -The paper [14] describes another technique to achieve acceleration in RMC. The acceleration operator is associated to cycles in the transition graph of the program.…”

“…Naturally, such a method will not be useful unless it terminates sufficiently often on practical examples. In order to achieve termination, several works adopt acceleration operators, the purpose of which is to compute (in one computation step) the effect of arbitrarily long sequences of transitions [1,14]. In general, the effect of acceleration is not computable.…”

Flat Petri Nets (Invited Talk)

“…Intuitively, acceleration techniques consist in computing symbolically the effect of iterating cycles of the system. Those techniques were studied for several models: systems with FIFO channels [11,15,16,10,9], time [3,2,12,13], other data structures [17], and systems manipulating counters including the VASS model [14,27,8,5,4,6,18,19].…”

Extrapolating (omega-)regular model checking

“…Among the techniques to compute accelerations, one distinguishes between domain specific and generic techniques. Domain-specific techniques [22] exploit the specific properties and representations of the domain being considered and were for instance obtained for systems with queues in [23,33], for systems with integers and reals in [19,25,31], for pushdown systems in [32,53], and for lossy queues in [4]. Generic techniques consider automata-based representations and provide algorithms that operate directly on these representations, mostly disregarding the domain for which it is used.…”