Filippo Bonchi

Checking NFA equivalence with bisimulations up to congruence

We introduce bisimulation up to congruence as a technique for proving language equivalence of non-deterministic finite automata. Exploiting this technique, we devise an optimisation of the classical algorithm by Hopcroft and Karp. We compare our approach to the recently introduced antichain algorithms, by analysing and relating the two underlying coinductive proof methods. We give concrete examples where we exponentially improve over antichains; experimental results moreover show non negligible improvements.

Generalizing Determinization from Automata to Coalgebras

The powerset construction is a standard method for converting a nondeter- ministic automaton into a deterministic one recognizing the same language. In this paper, we lift the powerset construction from automata to the more general framework of coal- gebras with structured state spaces. Coalgebra is an abstract framework for the uniform study of different kinds of dynamical systems. An endofunctor F determines both the type of systems (F-coalgebras) and a notion of behavioural equivalence (�F) amongst them. Many types of transition systems and their equivalences can be captured by a functor F. For example, for deterministic automata the derived equivalence is language equivalence, while for non-deterministic automata it is ordinary bisimilarity. We give several examples of applications of our generalized determinization construc- tion, including partial Mealy machines, (structured) Moore automata, Rabin probabilistic automata, and, somewhat surprisingly, even pushdown automata. To further witness the generality of the approach we show how to characterize coalgebraically several equivalences which have been object of interest in the concurrency community, such as failure or ready semantics.

Saturated Semantics for Reactive Systems

The semantics of process calculi has traditionally been specified by labelled transition systems (LTS), but with the development of name calculi it turned out that reaction rules (i.e., unlabelled transition rules) are often more natural. This leads to the question of how behavioural equivalences (bisimilarity, trace equivalence, etc.) defined for LTS can be transferred to unlabelled transition systems. Recently, in order to answer this question, several proposals have been made with the aim of automatically deriving an LTS from reaction rules in such a way that the resulting equivalences are congruences. Furthermore these equivalences should agree with the standard semantics, whenever one exists. In this paper we propose saturated semantics, based on a weaker notion of observation and orthogonal to all the previous proposals, and we demonstrate the appropriateness of our semantics by means of two examples: logic programming and a subset of the open pi-calculus. Indeed, we prove that our equivalences are congruences and that they coincide with logical equivalence and open bisimilarity respectively, while equivalences studied in previous works are strictly finer

Generalizing the powerset construction, coalgebraically

htmlabstractCoalgebra is an abstract framework for the uniform study of different kinds of dynamical systems. An endofunctor

A behavioural congruence for web services

F

Reactive Systems, Barbed Semantics, and the Mobile Ambients

determines both the type of systems (

Algebra-coalgebra duality in brzozowski's minimization algorithm

F

A coalgebraic perspective on minimization and determinization

-coalgebras) and a notion of behavioral equivalence (

Full Abstraction for Signal Flow Graphs

\sim_F

Process bisimulation via a graphical encoding

) amongst them. Many types of transition systems and their equivalences can be captured by a functor