Carla Piazza

An efficient algorithm for computing bisimulation equivalence

We propose an efficient algorithmic solution to the problem of determining a Bisimulation Relation on a finite structure working both on the explicit and on the implicit (symbolic) representation. As far as the explicit case is concerned, starting from a set-theoretic point of view we propose an algorithm that optimizes the solution to the Relational Coarsest Partition Problem given by Paige and Tarjan (SIAM J. Comput. 16(6) (1987) 973); its use in model-checking packages is also discussed and tested. For well-structured graphs our algorithm reaches a linear worst-case behaviour. The proposed algorithm is then re-elaborated to produce a symbolic version.

From Bisimulation to Simulation: Coarsest Partition Problems

The notions of bisimulation and simulation are used for graph reduction and are widely employed in many areas: modal logic, concurrency theory, set theory, formal verification, and so forth. In particular, in the context of formal verification they are used to tackle the so-called state-explosion problem. The faster algorithms to compute the maximum bisimulation on a given labeled graph are based on the crucial equivalence between maximum bisimulation and relational coarsest partition problem. As far as simulation is concerned, many algorithms have been proposed that turn out to be relatively inexpensive in terms of either time or space. In this paper we first revisit the state of the art about bisimulation and simulation, pointing out the analogies and differences between the two problems. Then, we propose a generalization of the relational coarsest partition problem, which is equivalent to the simulation problem. Finally, we present an algorithm that exploits such a characterization and improves on previously proposed algorithms for simulation.

Algorithmic algebraic model checking i: challenges from systems biology

In this paper, we suggest a possible confluence of the theory of hybrid automata and the techniques of algorithmic algebra to create a computational basis for systems biology. We describe a method to compute bounded reachability by combining Taylor polynomials and cylindric algebraic decomposition algorithms. We discuss the power and limitations of the framework we propose and we suggest several possible extensions. We briefly show an application to the study of the Delta-Notch protein signaling system in biology.

A Fast Bisimulation Algorithm

In this paper we propose an efficient algorithmic solution to the problem of determining a Bisimulation Relation on a finite structure. Starting from a set-theoretic point of view we propose an algorithm that optimizes the solution to the Relational coarsest Partition problem given by Paige and Tarjan in 1987 and its use in model-checking packages is briefly discussed and tested. Our algorithm reaches, in particular cases, a linear solution.

Modelling downgrading in information flow security

Information flow security properties such as noninterference ensure the protection of confidential data by strongly limiting the flow of sensitive information. However, to deal with real applications, it is often necessary to admit mechanisms for downgrading or declassifying information. In this paper, we propose a general unwinding framework for formalizing different noninterference properties permitting downgrading, i.e., allowing information to flow from a higher to a lower security level through a downgrader. The framework is parametric with respect to the observation equivalence used to discriminate between different process behaviours. We prove general compositionality properties and provide conditions under which both horizontal and vertical refinements are preserved under all the security properties obtained as instances of the unwinding framework. Finally, we present a decision procedure to check our security properties and prove some complexity results.

Algorithmic algebraic model checking II: decidability of semi-algebraic model checking and its applications to systems biology

Motivated by applications to systems biology, and the emergence of semi-algebraic hybrid systems as a natural framework for modeling biochemical networks, we continue exploring the decidability problem for model-checking with TCTL (Timed Computation Tree Logic) over this broad class of semi-algebraic hybrid systems. Previously, we had introduced these models, demonstrated the close connection to the goals of systems biology. However, we had only developed the techniques for bounded reachability, arguing for the adequacy of such an approach in a majority of the biological applications. Here, we present a semi-decidable symbolic algebraic dense-time TCTL model checking algorithm, which satisfies two desirable properties: it can be derived automatically from the symbolic description, and it extends to and generalizes other versions of temporal logics. The main mathematical device at the core of this approach is Tarski-Collins’ real quantifier elimination employed at each fixpoint iteration, whose high complexity is the crux of its unfortunate limitation. Along with these results, we prove the undecidability of this problem in the more powerful “real” Turing machine formalism of Blum, Shub and Smale. We then demonstrate a preliminary version of our model-checker Tolque on the Delta-Notch example.

Refinement operators and information flow security

The systematic development of complex systems usually relies on a stepwise refinement procedure from an abstract specification to a more concrete one that can finally be implemented. The use of refinement operators preserving system properties is clearly essential since it avoids properties to be re-investigated at each development step. In this paper, we formalize the notion of refinement for processes described as terms of the security process algebra (SPA). We consider several information flow security properties and provide sufficient conditions under which our refinement operators preserve such security properties. Finally, we study how refinements can be composed still preserving the security of the system.

Symbolic Graphs: Linear Solutions to Connectivity Related Problems

Abstract The importance of symbolic data structures such as Ordered Binary Decision Diagrams (OBDD) is rapidly growing in many areas of Computer Science where the large dimensions of the input models is a challenging feature: OBDD based graph representations allowed to define truly new standards in the achievable dimensions for the Model Checking verification technique. However, OBDD representations pose strict constraints in the algorithm design issue. For example, Depth-First Search (DFS) is not feasible in a symbolic framework and, consequently, many state-of-the-art DFS based algorithms (e.g., connectivity procedures) cannot be easily rearranged to work on symbolically represented graphs. We devise here a symbolic algorithmic strategy, based on the new notion of spine-set, that is general enough to be the engine of linear symbolic step algorithms for both strongly connected components and biconnected components. Our procedures improve on previously designed connectivity symbolic algorithms. Moreover, by an application to the so-called “bad cycle detection problem”, our technique can be used to efficiently solve the emptiness problem for various kinds of ω-automata.

Verifying persistent security properties

We study bisimulation-based information flow security properties which are persistent, in the sense that if a system is secure then all of its reachable states are secure too. We show that such properties can be characterized in terms of bisimulation-like equivalence relations, between the full system and the system prevented from performing confidential actions. Moreover, we provide a characterization of such properties in terms of unwinding conditions which demand properties of individual actions. These two different characterizations naturally lead to efficient methods for the verification and construction of secure systems. We also prove several compositionality results, that allow us to check the security of a system by only verifying the security of its subcomponents.

A uniform approach to constraint-solving for lists, multisets, compact lists, and sets

Lists, multisets, and sets are well-known data structures whose usefulness is widely recognized in various areas of computer science. They have been analyzed from an axiomatic point of view with a parametric approach in Dovier et al. [1998], where the relevant unification algorithms have been developed. In this article, we extend these results considering more general constraints, namely, equality and membership constraints and their negative counterparts.