Cristian Versari

Biochemical reaction rules with constraints

We propose React(C), an expressive programming language for stochastic modeling and simulation in systems biology that is based on biochemical reactions with constraints. We prove that React(C) can express the stochastic π-calculus, in contrast to previous rule-based programming languages, and further illustrate the high expressiveness of React(C). We present a stochastic simulator for React(C) independently of the choice of the constraint language C. Our simulator decides for a given reaction rule whether it can be applied to the current biochemical solution. We show that this decision problem is NP-complete for arbitrary constraint systems C and that it can be solved in polynomial time for rules of bounded arity. In practice, we propose to solve this problem by constraint programming.

Stochastic simulation of biological systems with dynamical compartment structure

The Gillespie stochastic simulation algorithm represents one of the main physical abstractions exploited for the simulation of biological systems modeled by means of concurrent calculi. While the faithful modelling of bio-systems often requires multi-compartment semantics, the original Gillespie algorithm considers only one fixed-size volume. In this paper we introduce an extended formalisation of the above algorithm which preserves the original model but allows the stochastic simulation in presence of multiple compartments with dynamical structure and variable sizes. The presented algorithm can be then used as basis for simulating systems expressed in an extended version of the stochastic π-Calculus, the Sπ@ language, obtained by means of polyadic synchronisation. Despite of its conservativeness, Sπ@ is showed to allow flexible modelling of multiple compartments with dynamical structure and to provide increased biological faithfulness.

π@: a π-based process calculus for the implementation of compartmentalised bio-inspired calculi

The modelling of biological systems led to the explicit introduction of compartments in several bio-oriented process calculi. In this tutorial we show how different compartment semantics can be obtained by means of a simple and conservative extension of the standard pi-calculus, the pi@ calculus. Significant examples are given through the encoding of two well known bio-inspired process calculi: BioAmbients and Brane Calculi.

Encoding Catalytic P Systems in π

P systems are theoretical computing devices abstracted away from the biological architecture of the cell, introduced some years ago by Gheorghe Paun and now intensely studied. In the area of concurrent systems, process calculi have recently been applied and extended with similar aim, to simulate (and formalise) the behaviour of the cell. Although many common points can be found between the two approaches, no formal and exhaustive comparison has been carried out yet. @p@ is a new calculus, strongly @p-Calculus based, well-suited to easily encode biologically inspired process calculi. In this paper the encoding in @p@ of one variant of P systems is proposed, thus allowing a better understanding of similarities between P systems and bio-inspired process calculi.

Introduction to Concurrency Theory

This introductory chapter outlines the main motivations for the study of concurrency theory and the differences with respect to the theory of sequential computation. It also reports the structure of the book and how to use it. Finally, some background material is briefly surveyed.

A Process Calculus for Expressing Finite Place/Transition Petri Nets

We introduce the process calculus Multi-CCS, which extends conservatively CCS with an operator of strong prefixing able to model atomic sequences of actions as well as multiparty synchronization. Multi-CCS is equipped with a labeled transition system semantics, which makes use of a minimal structural congruence. Multi-CCS is also equipped with an unsafe P/T Petri net semantics by means of a novel technique. This is the first rich process calculus, including CCS as a subcalculus, which receives a semantics in terms of unsafe, labeled P/T nets. The main result of the paper is that a class of Multi-CCS processes, called finite-net processes, is able to represent all finite (reduced) P/T nets.

Transition Systems and Behavioral Equivalences

Transition systems are introduced as a suitable semantic model of reactive systems. Some notions of behavioral equivalence are discussed, such as isomorphism equivalence, trace equivalence, simulation equivalence and bisimulation equivalence. Internal, unobservable actions are also considered and many behavioral equivalences are suitably adapted for this case.

CCS: A Calculus of Communicating Systems

The process calculus CCS for describing reactive systems is introduced. Its syntax is defined, as well as its operational semantics in terms of labeled transition systems. Some subcalculi are singled out that possess some specific interesting expressiveness properties. It is shown that CCS is Turing-complete by offering an encoding of Counter Machines into CCS. As a byproduct, all the behavioral equivalences of interest are undecidable over the class of CCS processes, even if they are decidable over some subcalculi.

An Operational Petri Net Semantics for A 2 CCS

A 2CCS is a conservative extension of CCS, enriched with an operator of strong prefixing, enabling the modeling of atomic sequences and multi-party synchronization (realized as an atomic sequence of binary synchronizations); the classic dining philosophers problem is used to illustrate the approach. A step semantics for A 2CCS is also presented directly as a labeled transition system. A safe Petri net semantics for this language is presented, following the approach of Degano, De Nicola, Montanari and Olderog. We prove that a process p and its associated net Net(p) are interleaving bisimilar (Theorem 5.1). Moreover, to support the claim that the intended concurrency is well-represented in the net, we also prove that a process p and its associated net Net(p) are step bisimilar (Theorem 5.2).

Algebraic Laws, Congruences and Axiomatizations

Behavioral equivalences, in particular those based on bisimulation, are shown to possess interesting algebraic laws. Moreover, we discuss which of them are congruences with respect to the CCS operators. Finally, behavioral congruences are axiomatized over finite CCS, and also finitely with the use of two auxiliary operators.