A False History of True Concurrency: From Petri to Tools

Abstract

Abstract. I briefly review the history of the unfolding approach to model checking.Carl Adam Petri passed away on July 2, 2010. I learnt about his death three days later, a few hours after finishing this text. He was a very profound and highly original thinker, and will be sadly missed. This note is dedicated to his memory.In some papers and talks, Moshe Vardi has described the history of the automatatheoretic approach to model checking, the verification technique that inspired the SPIN model checker and other tools. He traces it back to the work of theoreticians like Büchi, Prior, Trakhtenbrot and others, whose motivations were surprisingly far away from the applications that their ideas found down the line. Inspired by this work, in this note I briefly present the origins of the unfolding approach to model checking [21], a branch of the automata-theoretic approach that alleviates the state-explosion problem caused by concurrency.Since the unfolding approach is based on the theory of true concurrency, describing its origins requires to speak about the origin of true concurrency itself. However, here I only touch upon those aspects of the theory that directly inspired the unfolding approach. This leaves many important works out, and so this is a very partial and "false" history of true concurrency.The theory of true concurrency starts with two fundamental contributions by Carl Adam Petri, described in detail by Brauer and Reisig in an excellent article [11]. Both were a result of Petri's interest in analyzing the connection between mathematical, abstract computing machines, and their physical realizations. In his dissertation "Kommunikation mit Automaten", defended in 1962, Petri observes that the performance of a physically implemented Turing machine will degrade over time if the machine uses more and more storage space, because in this case signals have to travel longer and longer distances over longer and longer wires. To solve this problem he proposes an asynchronous architecture in which the storage space can be extended while the machine continues to operate. In the dissertation this abstract machine is described with the help of several semi-formal representations, but three years later Petri has already distilled the first mathematical formalism for asynchronous computation, and, arguably, the beginning of concurrency theory: Petri nets.Petri's second contribution is an analysis of the notion of execution of a machine as a sequence of global states, or as a sequence of events ordered by their occurrence times with respect to some global clock. He observes that global states or global clocks are again a mathematical construct that cannot be "implemented": since information can only travel at finite speed, no part of a system can know the state of all its components at a certain moment in time.1 He proposes to replace executions by nonsequential processes, sets of events ordered not by the time at which they occur, but by the causality relation, which is independent of the observer. The theory of nonsequen...

Quasi-Optimal Partial Order Reduction

“…Labelled Prime Event Structures. Prime event structures (pes) are well-known non-interleaving, partial-order semantics [16,8,7]. Let X be a set of actions.…”

“…The ⊆-maximal configurations of Fig. 2 (b) are [7] ∪ [17], [14], and [19]. Our algorithm starts at configuration C = ∅.…”

“…Recall that U has finitely many events, finitely many finite configurations, and no infinite configuration. Now, observe that the number of times that C i and C i+1 are related by l rather than r is finite, since every time Explore(·, ·, ·) makes a recursive call at line 10 it adds one event to C i , as stated by (7). More formally, the set L := {i ∈ N : C i l C i+1 } is finite.…”

Higher-Dimensional Timed Automata

“…Few such formalisms seem to be available in the literature. (The situation is perhaps best epitomized by the fact that there is a natural non-interleaving semantics for Petri nets (Goltz and Reisig, 1983) which is also used in practice (Esparza, 2010;Esparza and Heljanko, 2008), but almost all work on real-time extensions of Petri nets (Hanisch, 1993;Merlin and Farber, 1976;Sifakis, 1977;Srba, 2008), including the popular tool TAPAAL 1 , use an interleaving semantics.…”