Comparing Transition Systems with Independence and Asynchronous Transition Systems

Transition systems with independence and asynchronous transition systems are noninterleaving models for concurrency arising from the same simple idea of decorating transitions with events. They differ for the choice of a derived versus a primitive notion of event which induces considerable differences and makes the two models suitable for different purposes. This opens the problem of investigating their mutual relationships, to which this paper gives a fully comprehensive answer. In details, we characterise the category of extensional asynchronous transitions systems as the largest full subcategory of the category of (labelled) asynchronous transition systems which admits $TSI$, the category of transition systems with independence, as a coreflective subcategory. In addition, we introduce event-maximal asynchronous transitions systems and we show that their category is equivalent to $TSI$, so providing an exhaustive characterisation of transition systems with independence in terms of asynchronous transition systems

BDD Algortihms and Cache Misses

Within the last few years, CPU speed has greatly overtaken memory speed. For this reason, implementation of symbolic algorithms - with their extensive use of pointers and hashing - must be reexamined. In this paper, we introduce the concept of cache miss complexityas an analytical tool for evaluating algorithms depending on pointer chasing. Such algorithms are typical of symbolic computation found in verification. We show how this measure suggests new data structures and algorithmsfor multi-terminal BDDs. Our ideas have been implemented ina BDD package, which is used in a decision procedure for the Monadic Second-order Logic on strings.Experimental results show that on large examples involving e.g the verification of concurrent programs, our implementation runs 4 to 5 times faster than a widely used BDD implementation.We believe that the method of cache miss complexity is of general interest to any implementor of symbolic algorithms used in verification

An Equational Axiomatization for Multi-Exit Iteration

This paper presents an equational axiomatization of bisimulation equivalence over the language of Basic Process Algebra (BPA) with multi-exit iteration. Multi-exit iteration is a generalization of the standard binary Kleene star operation that allows for the specification of agents that, up to bisimulation equivalence, are solutionsof systems of recursion equations of the formX1 = P1 X2 + Q1...Xn = Pn X1 + Qnwhere n is a positive integer, and the Pi and the Qi are process terms. The additionof multi-exit iteration to BPA yields a more expressive language than that obtained by augmenting BPA with the standard binary Kleene star (BPA). As aconsequence, the proof of completeness of the proposed equational axiomatizationfor this language, although standard in its general structure, is much more involvedthan that for BPA. An expressiveness hierarchy for the family of k-exit iteration operators proposed by Bergstra, Bethke and Ponse is also offered.