Faron Moller

A temporal calculus of communicating systems

In this paper, we introduce a calculus of communicating systems which allows for the expression and analysis of timing constraints, for example as is important for real-time processes. We present the language, along with its formal semantics, and derive algebraic laws for reasoning about processes in the language. Though the core language is simple, we show that the language has several powerful derived operators which we demonstrate to be useful in several examples.

The Mobility Workbench - A Tool for the pi-Calculus

In this paper we describe the first prototype version of the Mobility Workbench (MWB), an automated tool for manipulating and analyzing mobile concurrent systems (those with evolving connectivity s ...

Verification on Infinite Structures

Abstract In this chapter, we present a hierarchy of infinite-state systems based on the primitive operations of sequential and parallel composition; the hierarchy includes a variety of commonly-studied classes of systems such as context-free and pushdown automata, and Petri net processes. We then examine the equivalence and regularity checking problems for these classes, with special emphasis on bisimulation equivalence, stressing the structural techniques which have been devised for solving these problems. Finally, we explore the model checking problem over these classes with respect to various linear- and branching-time temporal logics.

Bisimulation Equivalence is Decidable for Basic Parallel Processes

In a previous paper the authors proved the decidability of bisimulation equivalence over two subclasses of recursive processes involving a parallel composition operator, namely the so-called normed and live processes. In this paper, we extend this result to the whole class. The decidability proof permits us further to present a complete axiomatisation for this class of basic parallel processes. This result can be viewed as a proper extension of Milners complete axiomatisation of bisimulation equivalence on regular processes.

A polynomial-time algorithm for deciding bisimilation equivalence of normed Basic Parallel Processes

A polynomial-time algorithm is presented for deciding bisimulation equivalence of so-called Basic Parallel Processes: multisets of elementary processes combined by a commitative parallel-composition operator.

Relating Processes With Respect to Speed

In this paper, we consider the problem of defining a preorder on concurrent processes which will distinguish between functionally behaviourally equivalent processes which operate at different speeds. As our basic framework, we use a subset of the calculus TCCS of [Mol90], a language for describing concurrent processes involving timing constraints.

Checking Regular Properties of Petri Nets

In this paper we consider the problem of comparing an arbitrary Petri net against one whose places may contain only a bounded number of tokens (that is, against a regular behaviour), with respect to trace set inclusion and equivalence, as well as simulation and bisimulation. In contrast to the known result that language equivalence is undecidable, we find that all of the above are in fact decidable. We furthermore demonstrate that it is undecidable whether a given Petri net is either trace equivalent or simulation equivalent to any (unspecified) bounded net.

Unique decomposition of processes

Abstract In this paper, we examine questions about the prime decomposability of processes, where we define a process to be prime whenever it cannot be decomposed into nontrivial components. We show that any finite process can be uniquely decomposed into prime processes with respect to bisimulation equivalence, and demonstrate counterexamples to such a result for both failures (testing) equivalence and trace equivalence. Although we show that prime decompositions cannot exist for arbitrary infinite processes, we motivate but leave as open a conjecture on the unique decomposability of a wide subclass of infinite behaviours.

The Importance of the Left Merge Operator in Process Algebras

In this paper, we examine equational axiomatisations for PA, the process algebra of Bergstra and Klop, which is a simple subset of their full language ACP. The language PA has two combinators for concurrent execution: the usual full merge operator ∥ and the more esoteric left merge operator ⌊. Though this latter combinator is somewhat semantically unusual, we demonstrate its importance by proving that, whereas a finite sound and complete equational theory exists for PA, no such finite theory can exist for PA in the absence of the left merge operator.

Decomposability, decidability and axiomatisability for bisimulation equivalence on basic parallel processes

The authors prove the decidability of two subclasses of recursive processes involving a parallel composition operator with respect to bisimulation equivalence, namely, the so-called normed and live processes. To accomplish this, the authors first prove a unique decomposition result for (a generalization of) normed processes, in order to deduce a necessary cancellation law. The decidability proof leads to a complete axiomatization for these process classes.<<ETX>>