QUALITATIVE AND QUANTITATIVE FORMAL MODELING OF BIOLOGICAL SYSTEMS

Nella tesi si sviluppa un formalismo basato su riscrittura di termini e lo si propone come strumento per la descrizione di sistemi biologici. Tale formalismo, chiamato calculus of looping sequences (cls) consente di descrivere proteine, dna e membrane come termini, e interazioni tra questi elementi come regole di riscrittura. Diverse varianti di cls sono studiate al fine di descrivere diversi aspetti dei sistemi biologici, inoltre vengono definite equivalenze sul comportamento dei sistemi (bisimulazioni) e una versione stocastica del formalismo che consente di sviluppare strumenti di simulazione

A Type System for a Stochastic CLS

The Stochastic Calculus of Looping Sequences is suitable to describe the evolution of microbiological systems, taking into account the speed of the described activities. We propose a type system for this calculus that models how the presence of positive and negative catalysers can modify these speeds. We claim that types are the right abstraction in order to represent the interaction between elements without specifying exactly the element positions. Our claim is supported through an example modelling the lactose operon

Innocent strategies as presheaves and interactive equivalences for CCS

Seeking a general framework for reasoning about and comparing programming languages, we derive a new view of Milner's CCS. We construct a category E of plays, and a subcategory V of views. We argue that presheaves on V adequately represent innocent strategies, in the sense of game semantics. We then equip innocent strategies with a simple notion of interaction. This results in an interpretation of CCS. Based on this, we propose a notion of interactive equivalence for innocent strategies, which is close in spirit to Beffara's interpretation of testing equivalences in concurrency theory. In this framework we prove that the analogues of fair and must testing equivalences coincide, while they differ in the standard setting.Comment: In Proceedings ICE 2011, arXiv:1108.014

A Calculus for Molecular Interaction Maps

Molecular Interaction Maps are a graphical formalism used by biologists to describe complex interactions between molecules. We provide a formal description of MIMs using process algebras and determine its computational power

Decoding Choice Encodings

We study two encodings of the asynchronous pi-calculus with input-guarded choice into its choice-free fragment. One encoding is divergence-free, but refines the atomic commitment of choice into gradual commitment. The other preserves atomicity, but introduces divergence. The divergent encoding is fully abstract with respect to weak bisimulation, but the more natural divergence-free encoding is not. Instead, we show that it is fully abstract with respect to coupled simulation, a slightly coarser - but still coinductively defined - equivalence that does not enforce bisimilarity of internal branching decisions. The correctness proofs for the two choice encodings introduce a novel proof technique exploiting the properties of explicit decodings from translations to source terms

Reverse Bisimilarity vs. Forward Bisimilarity

Reversibility is the capability of a system of undoing its own actions starting from the last performed one, in such a way that a past consistent state is reached. This is not trivial for concurrent systems, as the last performed action may not be uniquely identifiable. There are several approaches to address causality-consistent reversibility, some including a notion of forward-reverse bisimilarity. We introduce a minimal process calculus for reversible systems to investigate compositionality properties and equational characterizations of forward-reverse bisimilarity as well as of its two components, i.e., forward bisimilarity and reverse bisimilarity, so as to highlight their differences. The study is conducted not only in a nondeterministic setting, but also in a stochastic one where time reversibility and lumpability for Markov chains are exploited

Topological Calculus of Looping Sequences

Il Calculus of Looping Sequences (CLS) permette la descrizione dei sistemi biologici e della loro evoluzione. Nell'ambito del lavoro di tesi e' stata sviluppata una estensione del CLS, chiamata Topological CLS (TCLS), dove ad ogni oggetto del sistema biologico sono associate una precisa posizione e dimensione nello spazio. Gli oggetti possono muoversi autonomamente e l'applicabilita' delle regole di riscrittura, che modellano le reazioni tra gli elementi, puo' essere determinata dalle posizioni degli oggetti coinvolti. Infine, alle regole di riscrittura e' associato un parametro che ne specifica la velocita' di reazione. Il Topological CLS e' stato quindi utilizzato per modellare due esempi di sistemi biologici: il processo di mitosi e il quorum-sensing