Ackermann Encoding, Bisimulations, and OBDDs

We propose an alternative way to represent graphs via OBDDs based on the observation that a partition of the graph nodes allows sharing among the employed OBDDs. In the second part of the paper we present a method to compute at the same time the quotient w.r.t. the maximum bisimulation and the OBDD representation of a given graph. The proposed computation is based on an OBDD-rewriting of the notion of Ackermann encoding of hereditarily finite sets into natural numbers.Comment: To appear on 'Theory and Practice of Logic Programming

Approximated Symbolic Computations over Hybrid Automata

Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the real systems and infinite precision measurements. Such assumptions are not only unrealistic, but often lead to the construction of misleading models. For these reasons we believe that it is necessary to introduce more flexible semantics able to manage with noise, partial information, and finite precision instruments. In particular, in this paper we integrate in a single framework based on approximated semantics different over and under-approximation techniques for hybrid automata. Our framework allows to both compare, mix, and generalize such techniques obtaining different approximated reachability algorithms.Comment: In Proceedings HAS 2013, arXiv:1308.490

Unwinding biological systems

Unwinding conditions have been fruitfully exploited in Information Flow Security to define persistent security properties. In this paper we investigate their meaning and possible uses in the analysis of biological systems. In particular, we elaborate on the notion of robustness and propose some instances of unwinding over the process algebra Bio-PEPA and over hybrid automata. We exploit such instances to analyse two case-studies: Neurospora crassa circadian system and Influenza kinetics models

Checking Integrity via CoPS and Banana: the E-Commerce Case Study

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Hybrid Automata in Systems Biology: How far can we go?

We consider the reachability problem on semi-algebraic hybrid automata. In particular, we deal with the effective cost that has to be afforded to solve reachability through first-order satisfiability. The analysis we perform with some existing tools shows that even simple examples cannot be efficiently solved. We need approximations to reduce the number of variables in our formulae: this is the main source of time computation growth. We study standard approximation methods based on Taylor polynomials and ad-hoc strategies to solve the problem and we show their effectiveness on the repressilator case study

External Control in Process Algebra for Systems Biology

A critical aspect in the modeling of biological systems is the description view point. On the one hand, the Stochastic \u3c0-calculus formalism provides an intuitive and compact representation from an internal perspective. On the other hand, other proposed languages such as Hybrid Automata and Stochastic Concurrent Constraint Programming introduce in the system description an external control and provide more structured models. This work aims at bridging the above discussed gap. In particular, we propose a different approach for the encoding of biological systems in Stochastic \u3c0-calculus in the direction of introducing an external control and comparing different formalisms. We show the effectiveness of our method on some examples

Discrete Semantics for Hybrid Automata

Many natural systems exhibit a hybrid behavior characterized by a set of continuous laws which are switched by discrete events. Such behaviors can be described in a very natural way by a class of automata called hybrid automata. Their evolution are represented by both dynamical systems on dense domains and discrete transitions. Once a real system is modeled in a such framework, one may want to analyze it by applying automatic techniques, such as Model Checking or Abstract Interpretation. Unfortunately, the discrete/continuous evolutions not only provide hybrid automata of great flexibility, but they are also at the root of many undecidability phenomena. This paper addresses issues regarding the decidability of the reachability problem for hybrid automata (i.e., "can the system reach a state a from a state b?") by proposing an "inaccurate" semantics. In particular, after observing that dense sets are often abstractions of real world domains, we suggest, especially in the context of biological simulation, to avoid the ability of distinguishing between values whose distance is less than a fixed \u3b5. On the ground of the above considerations, we propose a new semantics for first-order formul\ue6 which guarantees the decidability of reachability. We conclude providing a paradigmatic biological example showing that the new semantics mimics the real world behavior better than the precise one

Is Hyper-extensionality Preservable Under Deletions of Graph Elements?

Any hereditarily finite set S can be represented as a finite pointed graph \u2013dubbed membership graph\u2013 whose nodes denote elements of the transitive closure of {S} and whose edges model the membership relation. Membership graphs must be hyper-extensional, that is pairwise distinct nodes are not bisimilar and (uniquely) represent hereditarily finite sets. We will see that the removal of even a single node or edge from a membership graph can cause \u201ccollapses\u201d of different nodes and, therefore, the loss of hyper-extensionality of the graph itself. With the intent of gaining a deeper understanding on the class of hyper-extensional hereditarily finite sets, this paper investigates whether pointed hyper-extensional graphs always contain either a node or an edge whose removal does not disrupt the hyper-extensionality property