The Logical View on Continuous Petri Nets

International audienceContinuous Petri nets are a relaxation of classical discrete Petri nets in which transitions can be fired a fractional number of times, and consequently places may contain a fractional number of tokens. Such continuous Petri nets are an appealing object to study since they over approximate the set of reachable configurations of their discrete counterparts, and their reachability problem is known to be decidable in polynomial time. The starting point of this paper is to show that the reachability relation for continuous Petri nets is definable by a sentence of linear size in the existential theory of the rationals with addition and order. Using this characterization, we obtain decidability and complexity results for a number of classical decision problems for continuous Petri nets. In particular, we settle the open problem about the precise complexity of reachability set inclusion. Finally, we show how continuous Petri nets can be incorporated inside the classical backward coverability algorithm for discrete Petri nets as a pruning heuristic in order to tackle the symbolic state explosion problem. The cornerstone of the approach we present is that our logical characterization enables us to leverage the power of modern SMT-solvers in order to yield a highly performant and robust decision procedure for coverability in Petri nets. We demonstrate the applicability of our approach on a set of standard benchmarks from the literature

A structured approach for the engineering of biochemical network models, illustrated for signalling pathways

http://dx.doi.org/10.1093/bib/bbn026Quantitative models of biochemical networks (signal transduction cascades, metabolic pathways, gene regulatory circuits) are a central component of modern systems biology. Building and managing these complex models is a major challenge that can benefit from the application of formal methods adopted from theoretical computing science. Here we provide a general introduction to the field of formal modelling, which emphasizes the intuitive biochemical basis of the modelling process, but is also accessible for an audience with a background in computing science and/or model engineering. We show how signal transduction cascades can be modelled in a modular fashion, using both a qualitative approach { Qualitative Petri nets, and quantitative approaches { Continuous Petri Nets and Ordinary Differential Equations. We review the major elementary building blocks of a cellular signalling model, discuss which critical design decisions have to be made during model building, and present ..

An Effective Fixpoint Semantics for Linear Logic Programs

In this paper we investigate the theoretical foundation of a new bottom-up semantics for linear logic programs, and more precisely for the fragment of LinLog that consists of the language LO enriched with the constant 1. We use constraints to symbolically and finitely represent possibly infinite collections of provable goals. We define a fixpoint semantics based on a new operator in the style of Tp working over constraints. An application of the fixpoint operator can be computed algorithmically. As sufficient conditions for termination, we show that the fixpoint computation is guaranteed to converge for propositional LO. To our knowledge, this is the first attempt to define an effective fixpoint semantics for linear logic programs. As an application of our framework, we also present a formal investigation of the relations between LO and Disjunctive Logic Programming. Using an approach based on abstract interpretation, we show that DLP fixpoint semantics can be viewed as an abstraction of our semantics for LO. We prove that the resulting abstraction is correct and complete for an interesting class of LO programs encoding Petri Nets.Comment: 39 pages, 5 figures. To appear in Theory and Practice of Logic Programmin

Model Checking Linear Logic Specifications

The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear logic programming language called LO enriched with universally quantified goal formulas. Although LO was originally introduced as a theoretical foundation for extensions of logic programming languages, it can also be viewed as a very general language to specify a wide range of infinite-state concurrent systems. Our approach is based on the relation between backward reachability and provability highlighted in our previous work on propositional LO programs. Following this line of research, we define here a general framework for the bottom-up evaluation of first order linear logic specifications. The evaluation procedure is based on an effective fixpoint operator working on a symbolic representation of infinite collections of first order linear logic formulas. The theory of well quasi-orderings can be used to provide sufficient conditions for the termination of the evaluation of non trivial fragments of first order linear logic.Comment: 53 pages, 12 figures "Under consideration for publication in Theory and Practice of Logic Programming

MathMC: A mathematica-based tool for CSL model checking of deterministic and stochastic Petri nets

Deterministic and Stochastic Petri Nets (DSPNs) are a widely used high-level formalism for modeling discreteevent systems where events may occur either without consuming time, after a deterministic time, or after an exponentially distributed time. CSL (Continuous Stochastic Logic) is a (branching) temporal logic developed to express probabilistic properties in continuous time Markov chains (CTMCs). In this paper we present a Mathematica-based tool that implements recent developments for model checking CSL style properties on DSPNs. Furthermore, as a consequence of the type of process underlying DSPNs (a superset of Markovian processes), we are also able to check CSL properties of Generalized Stochastic Petri Nets (GSPNs) and labeled CTMCs

A review of information flow diagrammatic models for product-service systems

A product-service system (PSS) is a combination of products and services to create value for both customers and manufacturers. Modelling a PSS based on function orientation offers a useful way to distinguish system inputs and outputs with regards to how data are consumed and information is used, i.e. information flow. This article presents a review of diagrammatic information flow tools, which are designed to describe a system through its functions. The origin, concept and applications of these tools are investigated, followed by an analysis of information flow modelling with regards to key PSS properties. A case study of selection laser melting technology implemented as PSS will then be used to show the application of information flow modelling for PSS design. A discussion based on the usefulness of the tools in modelling the key elements of PSS and possible future research directions are also presented