Vector Addition System Reversible Reachability Problem

The reachability problem for vector addition systems is a central problem of net theory. This problem is known to be decidable but the complexity is still unknown. Whereas the problem is EXPSPACE-hard, no elementary upper bounds complexity are known. In this paper we consider the reversible reachability problem. This problem consists to decide if two configurations are reachable one from each other, or equivalently if they are in the same strongly connected component of the reachability graph. We show that this problem is EXPSPACE-complete. As an application of the introduced materials we characterize the reversibility domains of a vector addition system

Analysis of Petri Nets and Transition Systems

This paper describes a stand-alone, no-frills tool supporting the analysis of (labelled) place/transition Petri nets and the synthesis of labelled transition systems into Petri nets. It is implemented as a collection of independent, dedicated algorithms which have been designed to operate modularly, portably, extensibly, and efficiently.Comment: In Proceedings ICE 2015, arXiv:1508.0459

Petri nets for systems and synthetic biology

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which uni¯es the qualita- tive, stochastic and continuous paradigms. Each perspective adds its con- tribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how quali- tative descriptions are abstractions over stochastic or continuous descrip- tions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks

Petri net equivalence

Determining whether two Petri nets are equivalent is an interesting problem from both practical and theoretical standpoints. Although it is undecidable in the general case, for many interesting nets the equivalence problem is solvable. This paper explores, mostly from a theoretical point of view, some of the issues of Petri net equivalence, including both reachability sets and languages. Some new definitions of reachability set equivalence are described which allow the markings of some places to be treated identically or ignored, analogous to the Petri net languages in which multiple transitions may be labeled with the same symbol or with the empty string. The complexity of some decidable Petri net equivalence problems is analyzed

On functional module detection in metabolic networks

Functional modules of metabolic networks are essential for understanding the metabolism of an organism as a whole. With the vast amount of experimental data and the construction of complex and large-scale, often genome-wide, models, the computer-aided identification of functional modules becomes more and more important. Since steady states play a key role in biology, many methods have been developed in that context, for example, elementary flux modes, extreme pathways, transition invariants and place invariants. Metabolic networks can be studied also from the point of view of graph theory, and algorithms for graph decomposition have been applied for the identification of functional modules. A prominent and currently intensively discussed field of methods in graph theory addresses the Q-modularity. In this paper, we recall known concepts of module detection based on the steady-state assumption, focusing on transition-invariants (elementary modes) and their computation as minimal solutions of systems of Diophantine equations. We present the Fourier-Motzkin algorithm in detail. Afterwards, we introduce the Q-modularity as an example for a useful non-steady-state method and its application to metabolic networks. To illustrate and discuss the concepts of invariants and Q-modularity, we apply a part of the central carbon metabolism in potato tubers (Solanum tuberosum) as running example. The intention of the paper is to give a compact presentation of known steady-state concepts from a graph-theoretical viewpoint in the context of network decomposition and reduction and to introduce the application of Q-modularity to metabolic Petri net models

A recursive paradigm for aligning observed behavior of large structured process models

The alignment of observed and modeled behavior is a crucial problem in process mining, since it opens the door for conformance checking and enhancement of process models. The state of the art techniques for the computation of alignments rely on a full exploration of the combination of the model state space and the observed behavior (an event log), which hampers their applicability for large instances. This paper presents a fresh view to the alignment problem: the computation of alignments is casted as the resolution of Integer Linear Programming models, where the user can decide the granularity of the alignment steps. Moreover, a novel recursive strategy is used to split the problem into small pieces, exponentially reducing the complexity of the ILP models to be solved. The contributions of this paper represent a promising alternative to fight the inherent complexity of computing alignments for large instances.Peer ReviewedPostprint (author's final draft

Distance Between Mutually Reachable Petri Net Configurations

Petri nets are a classical model of concurrency widely used and studied in formal verification with many applications in modeling and analyzing hardware and software, data bases, and reactive systems. The reachability problem is central since many other problems reduce to reachability questions. In 2011, we proved that a variant of the reachability problem, called the reversible reachability problem is exponential-space complete. Recently, this problem found several unexpected applications in particular in the theory of population protocols. In this paper we revisit the reversible reachability problem in order to prove that the minimal distance in the reachability graph of two mutually reachable configurations is linear with respect to the Euclidean distance between those two configurations

Flat counter automata almost everywhere!

This paper argues that flatness appears as a central notion in the verification of counter automata. A counter automaton is called flat when its control graph can be ``replaced\u27\u27, equivalently w.r.t. reachability, by another one with no nested loops. From a practical view point, we show that flatness is a necessary and sufficient condition for termination of accelerated symbolic model checking, a generic semi-algorithmic technique implemented in successful tools like FAST, LASH or TReX. From a theoretical view point, we prove that many known semilinear subclasses of counter automata are flat: reversal bounded counter machines, lossy vector addition systems with states, reversible Petri nets, persistent and conflict-free Petri nets, etc. Hence, for these subclasses, the semilinear reachability set can be computed using a emph{uniform} accelerated symbolic procedure (whereas previous algorithms were specifically designed for each subclass)

A lambda calculus for quantum computation with classical control

The objective of this paper is to develop a functional programming language for quantum computers. We develop a lambda calculus for the classical control model, following the first author's work on quantum flow-charts. We define a call-by-value operational semantics, and we give a type system using affine intuitionistic linear logic. The main results of this paper are the safety properties of the language and the development of a type inference algorithm.Comment: 15 pages, submitted to TLCA'05. Note: this is basically the work done during the first author master, his thesis can be found on his webpage. Modifications: almost everything reformulated; recursion removed since the way it was stated didn't satisfy lemma 11; type inference algorithm added; example of an implementation of quantum teleportation adde