Graph models for reachability analysis of concurrent programs

Reachability analysis is an attractive technique for analysis of concurrent programs because it is simple and relatively straightforward to automate, and can be used in conjunction with model-checking procedures to check for application-specific as well as general properties. Several techniques have been proposed differing mainly on the model used; some of these propose the use of flowgraph based models, some others of Petri nets.This paper addresses the question: What essential difference does it make, if any, what sort of finite-state model we extract from program texts for purposes of reachability analysis? How do they differ in expressive power, decision power, or accuracy? Since each is intended to model synchronization structure while abstracting away other features, one would expect them to be roughly equivalent.We confirm that there is no essential semantic difference between the most well known models proposed in the literature by providing algorithms for translation among these models. This implies that the choice of model rests on other factors, including convenience and efficiency.Since combinatorial explosion is the primary impediment to application of reachability analysis, a particular concern in choosing a model is facilitating divide-and-conquer analysis of large programs. Recently, much interest in finite-state verification systems has centered on algebraic theories of concurrency. Yeh and Young have exploited algebraic structure to decompose reachability analysis based on a flowgraph model. The semantic equivalence of graph and Petri net based models suggests that one ought to be able to apply a similar strategy for decomposing Petri nets. We show this is indeed possible through application of category theory

Formal Relationships Between Geometrical and Classical Models for Concurrency

A wide variety of models for concurrent programs has been proposed during the past decades, each one focusing on various aspects of computations: trace equivalence, causality between events, conflicts and schedules due to resource accesses, etc. More recently, models with a geometrical flavor have been introduced, based on the notion of cubical set. These models are very rich and expressive since they can represent commutation between any bunch of events, thus generalizing the principle of true concurrency. While they seem to be very promising - because they make possible the use of techniques from algebraic topology in order to study concurrent computations - they have not yet been precisely related to the previous models, and the purpose of this paper is to fill this gap. In particular, we describe an adjunction between Petri nets and cubical sets which extends the previously known adjunction between Petri nets and asynchronous transition systems by Nielsen and Winskel

A survey of petri nets slicing

Petri nets slicing is a technique that aims to improve the verification of systems modeled in Petri nets. Petri nets slicing was first developed to facilitate debugging but then used for the alleviation of the state space explosion problem for the model checking of Petri nets. In this article, different slicing techniques are studied along with their algorithms introducing: i) a classification of Petri nets slicing algorithms based on their construction methodology and objective (such as improving state space analysis or testing), ii) a qualitative and quantitative discussion and comparison of major differences such as accuracy and efficiency, iii) a syntactic unification of slicing algorithms that improve state space analysis for easy and clear understanding, and iv) applications of slicing for multiple perspectives. Furthermore, some recent improvements to slicing algorithms are presented, which can certainly reduce the slice size even for strongly connected nets. A noteworthy use of this survey is for the selection and improvement of slicing techniques for optimizing the verification of state event models

Application of an Exact Transversal Hypergraph in Selection of SM-Components

Part 9: Embedded Systems and Petri NetsInternational audienceThe paper deals with the application of the hypergraph theory in selection of State Machine Components (SM-Components) of Petri nets [1,2].As it is known, Petri nets are widely used for modeling of concurrency processes. However, in order to implement the concurrent automaton, an initial Petri net ought to be decomposed into sequential automata (SM-Components), which can be easily designed as an Finite-State-Machine (FSM) or Microprogrammed Controller [3]. The last step of the decomposition process of the Petri nets is selection of SM-Components. This stage is especially important because it determines the final number of sequential automata. In the article we propose a new idea of SM-Components selection. The aim of the method is reduction of the computational complexity from exponential to polynomial. Such a reduction can be done if the selection hypergraph belongs to the exact transversal hypergraphs (xt-hypergraphs) class. Since the recognition and generation of the first transversal in the xt-hypergraphs are both polynomial, the complete selection process can be performed in polynomial time. The proposed ideas are an extension of the concept presented in [1].The proposed method has been verified experimentally. The conducted investigations have shown that for more than 85% of examined Petri nets the selection process can be done via xt-hypergraphs

Application of hypergraphs in decomposition of discrete systems

seria: Lecture Notes in Control and Computer Science ; vol. 23

Safety verification of asynchronous pushdown systems with shaped stacks

In this paper, we study the program-point reachability problem of concurrent pushdown systems that communicate via unbounded and unordered message buffers. Our goal is to relax the common restriction that messages can only be retrieved by a pushdown process when its stack is empty. We use the notion of partially commutative context-free grammars to describe a new class of asynchronously communicating pushdown systems with a mild shape constraint on the stacks for which the program-point coverability problem remains decidable. Stacks that fit the shape constraint may reach arbitrary heights; further a process may execute any communication action (be it process creation, message send or retrieval) whether or not its stack is empty. This class extends previous computational models studied in the context of asynchronous programs, and enables the safety verification of a large class of message passing programs

Modelling Mutual Exclusion in a Process Algebra with Time-outs

I show that in a standard process algebra extended with time-outs one can correctly model mutual exclusion in such a way that starvation-freedom holds without assuming fairness or justness, even when one makes the problem more challenging by assuming memory accesses to be atomic. This can be achieved only when dropping the requirement of speed independence.Comment: arXiv admin note: text overlap with arXiv:2008.1335

Decidable Models of Recursive Asynchronous Concurrency

Asynchronously communicating pushdown systems (ACPS) that satisfy the empty-stack constraint (a pushdown process may receive only when its stack is empty) are a popular decidable model for recursive programs with asynchronous atomic procedure calls. We study a relaxation of the empty-stack constraint for ACPS that permits concurrency and communication actions at any stack height, called the shaped stack constraint, thus enabling a larger class of concurrent programs to be modelled. We establish a close connection between ACPS with shaped stacks and a novel extension of Petri nets: Nets with Nested Coloured Tokens (NNCTs). Tokens in NNCTs are of two types: simple and complex. Complex tokens carry an arbitrary number of coloured tokens. The rules of NNCT can synchronise complex and simple tokens, inject coloured tokens into a complex token, and eject all tokens of a specified set of colours to predefined places. We show that the coverability problem for NNCTs is Tower-complete. To our knowledge, NNCT is the first extension of Petri nets, in the class of nets with an infinite set of token types, that has primitive recursive coverability. This result implies Tower-completeness of coverability for ACPS with shaped stacks