Reachability in Cooperating Systems with Architectural Constraints is PSPACE-Complete

The reachability problem in cooperating systems is known to be PSPACE-complete. We show here that this problem remains PSPACE-complete when we restrict the communication structure between the subsystems in various ways. For this purpose we introduce two basic and incomparable subclasses of cooperating systems that occur often in practice and provide respective reductions. The subclasses we consider consist of cooperating systems the communication structure of which forms a line respectively a star.Comment: In Proceedings GRAPHITE 2013, arXiv:1312.706

Interaction Systems and 1-safe Petri Nets

Interaction systems are a formal model for component-based systems, where components are combined via connectors to form more complex systems. We compare interaction systems (IS) to the wellstudied model of 1-safe Petri nets (1SN) by giving a translation map1: 1SN → IS and a translation map2: IS → 1SN, so that a 1-safe Petri net (an interaction system) and its according interaction system (1-safe Petri net) defined by the respective mapping are isomorphic up to some label relation R. So in some sense both models share the same expressiveness. Also, the encoding map1 is polynomial and can be used to reduce the problems of reachability, deadlock and liveness in 1SN to the problems of reachability, deadlock and liveness in IS, yielding PSPACE-hardness for these questions

Deriving Petri nets from finite transition systems

This paper presents a novel method to derive a Petri net from any specification model that can be mapped into a state-based representation with arcs labeled with symbols from an alphabet of events (a Transition System, TS). The method is based on the theory of regions for Elementary Transition Systems (ETS). Previous work has shown that, for any ETS, there exists a Petri Net with minimum transition count (one transition for each label) with a reachability graph isomorphic to the original Transition System. Our method extends and implements that theory by using the following three mechanisms that provide a framework for synthesis of safe Petri nets from arbitrary TSs. First, the requirement of isomorphism is relaxed to bisimulation of TSs, thus extending the class of synthesizable TSs to a new class called Excitation-Closed Transition Systems (ECTS). Second, for the first time, we propose a method of PN synthesis for an arbitrary TS based on mapping a TS event into a set of transition labels in a PN. Third, the notion of irredundant region set is exploited, to minimize the number of places in the net without affecting its behavior. The synthesis method can derive different classes of place-irredundant Petri Nets (e.g., pure, free choice, unique choice) from the same TS, depending on the constraints imposed on the synthesis algorithm. This method has been implemented and applied in different frameworks. The results obtained from the experiments have demonstrated the wide applicability of the method.Peer ReviewedPostprint (published version

Process windows

We describe a method for formally representing the behaviour of complex processes by process windows. Each window covers a part of the system behaviour, i.e. a part of the underlying transition system, and is easier to understand and analyse than the complete transition system. Process windows can overlap and have shared states and transitions so that the complete system behaviour is the union of window behaviours. We demonstrate the advantage of such representations when dealing with complex system behaviours, and discuss potential applications in circuit design and process mining. As a motivational example we consider the problem of covering transition systems by marked graphs, or more generally choicefree Petri nets. The obtained windows correspond to choice-free behavioural scenarios of the system, wherein one window can take over, or wake up, after another window has become inactive. The corresponding wake-up conditions and wake-up markings can be derived automatically.Peer ReviewedPostprint (author's final draft

Incorporating negative information to process discovery of complex systems

The discovery of a formal process model from event logs describing real process executions is a challenging problem that has been studied from several angles. Most of the contributions consider the extraction of a model as a one-class supervised learning problem where only a set of process instances is available. Moreover, the majority of techniques cannot generate complex models, a crucial feature in some areas like manufacturing. In this paper we present a fresh look at process discovery where undesired process behaviors can also be taken into account. This feature may be crucial for deriving process models which are less complex, fitting and precise, but also good on generalizing the right behavior underlying an event log. The technique is based on the theory of convex polyhedra and satisfiability modulo theory (SMT) and can be combined with other process discovery approach as a post processing step to further simplify complex models. We show in detail how to apply the proposed technique in combination with a recent method that uses numerical abstract domains. Experiments performed in a new prototype implementation show the effectiveness of the technique and the ability to be combined with other discovery techniques.Peer ReviewedPostprint (author's final draft

Synthesis of asynchronous controllers using integer linear programming

A novel strategy for the logic synthesis of asynchronous control circuits is presented. It is based on the structural theory of Petri nets and integer linear programming. Techniques that are capable of checking implementability conditions, such as complete state coding, and deriving a gate netlist to implement the specified behavior are presented. These techniques can handle Petri net specifications consisting of several thousands of transitions and provide a significant speed-up compared with techniques that have previously been proposed.Peer ReviewedPostprint (published version

A Rice-style theorem for parallel automata

AbstractWe present a general result, similar to Rice’s theorem, concerning the complexity of detecting properties on finite automata enriched by bounded cooperative concurrency, such as statecharts and abstract parallel automata, which we denote by CFAs (Concurrent Finite Automata). On one extreme, the complexity of detecting non-trivial properties that preserve equivalence of machines, i.e. properties of the accepted language, on finite automata, can be as little as O(1). On the other extreme, Rice’s theorem states that all such properties on Turing machines are undecidable. We state that all the non-trivial properties of the regular (or ω-regular) languages, are PSPACE-hard on CFAs with ϵ-moves and on CFAs without ϵ-moves accepting infinite words. We also extend this result to CFAs without ϵ-moves accepting finite words that satisfy a condition that holds for many properties

Bisimilarity and Behaviour-Preserving Reconfigurations of Open Petri Nets

We propose a framework for the specification of behaviour-preserving reconfigurations of systems modelled as Petri nets. The framework is based on open nets, a mild generalisation of ordinary Place/Transition nets suited to model open systems which might interact with the surrounding environment and endowed with a colimit-based composition operation. We show that natural notions of bisimilarity over open nets are congruences with respect to the composition operation. The considered behavioural equivalences differ for the choice of the observations, which can be single firings or parallel steps. Additionally, we consider weak forms of such equivalences, arising in the presence of unobservable actions. We also provide an up-to technique for facilitating bisimilarity proofs. The theory is used to identify suitable classes of reconfiguration rules (in the double-pushout approach to rewriting) whose application preserves the observational semantics of the net.Comment: To appear in "Logical Methods in Computer Science", 41 page

Decomposition of transition systems into sets of synchronizing state machines

Transition systems (TS) and Petri nets (PN) are important models of computation ubiquitous in formal methods for modeling systems. An important problem is how to extract from a given TS a PN whose reachability graph is equivalent (with a suitable notion of equivalence) to the original TS. This paper addresses the decomposition of transition systems into synchronizing state machines (SMs), which are a class of Petri nets where each transition has one incoming and one outgoing arc and all markings have exactly one token. This is an important case of the general problem of extracting a PN from a TS. The decomposition is based on the theory of regions, and it is shown that a property of regions called excitation-closure is a sufficient condition to guarantee the equivalence between the original TS and a decomposition into SMs. An efficient algorithm is provided which solves the problem by reducing its critical steps to the maximal independent set problem (to compute a minimal set of irredundant SMs) or to satisfiability (to merge the SMs). We report experimental results that show a good trade-off between quality of results vs. computation time

Automating synthesis of asynchronous communication mechanisms

Asynchronous data communication mechanisms (ACMs) have been extensively studied as data connectors between independently timed processes in digital systems. In previous work, systematic ACM synthesis methods have been proposed. In this paper, we advance this work by developing algorithms and software tools which automate the major part of the ACM synthesis process. Firstly, an interleaving specification is constructed in the form of a state graph, and secondly, a Petri net model of an "ACM-type" is derived using the notion of an ACM-region. The method is applied to a number of "standard" writing and reading policies of ACMs with shared memory and unidirectional control variables.Peer ReviewedPostprint (published version