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In the context of combinations of theories with disjoint signatures, we classify the component theories according to the decidability of constraint satisfiability problems in arbitrary and in infinite models, respectively. We exhibit a theory T1 such that satisfiability is decidable, but satisfiability in infinite models is undecidable. It follows that… (More)

- Silvio Ghilardi, Enrica Nicolini, Silvio Ranise, Daniele Zucchelli
- IJCAR
- 2008

We introduce the notion of array-based system as a suitable abstraction of infinite state systems such as broadcast protocols or sorting programs. By using a class of quantified-first order formulae to symbolically represent array-based systems, we propose methods to check safety (invariance) and liveness (recurrence) properties on top of Satisfiability… (More)

- Silvio Ghilardi, Enrica Nicolini, Silvio Ranise, Daniele Zucchelli
- Annals of Mathematics and Artificial Intelligence
- 2007

The theory of arrays, introduced by McCarthy in his seminal paper “Towards a mathematical science of computation,” is central to Computer Science. Unfortunately, the theory alone is not sufficient for many important verification applications such as program analysis. Motivated by this observation, we study extensions of the theory of arrays whose… (More)

- Silvio Ghilardi, Enrica Nicolini, Daniele Zucchelli
- FroCoS
- 2005

We define a general notion of a fragment within higher order type theory; a procedure for constraint satisfiability in combined fragments is outlined, following Nelson-Oppen schema. The procedure is in general only sound, but it becomes terminating and complete when the shared fragment enjoys suitable noetherianity conditions and allows an abstract version… (More)

- Silvio Ghilardi, Enrica Nicolini, Daniele Zucchelli
- ACM Trans. Comput. Log.
- 2008

We define a general notion of a fragment within higher-order type theory; a procedure for constraint satisfiability in combined fragments is outlined, following Nelson-Oppen schema. The procedure is in general only sound, but it becomes terminating and complete when the shared fragment enjoys suitable noetherianity conditions and admits an abstract version… (More)

Manna and Pnueli have extensively shown how a mixture of first-order logic (FOL) and discrete Linear time Temporal Logic (LTL) is sufficient to precisely state verification problems for the class of reactive systems. Theories in FOL model the (possibly infinite) data structures used by a reactive system while LTL specifies its (dynamic) behavior. In this… (More)

The design of decision procedures for combinations of theories sharing some arithmetic fragment is a challenging problem in verification. One possible solution is to apply a combination method à la Nelson-Oppen, like the one developed by Ghilardi for unions of non-disjoint theories. We show how to apply this non-disjoint combination method with the theory… (More)

We present a novel technique to combine satisfiability procedures for theories that model some data-structures and that share the integer offsets. This procedure extends the Nelson-Oppen approach to a family of non-disjoint theories that have practical interest in verification. The result is derived by showing that the considered theories satisfy the… (More)

- Silvio Ghilardi, Enrica Nicolini, Silvio Ranise, Daniele Zucchelli
- JELIA
- 2006

The theory of arrays, introduced by McCarthy in his seminal paper “Toward a mathematical science of computation”, is central to Computer Science. Unfortunately, the theory alone is not sufficient for many important verification applications such as program analysis. Motivated by this observation, we study extensions of the theory of arrays whose… (More)

- Enrica Nicolini, Christophe Ringeissen, Michaël Rusinowitch
- Fundam. Inform.
- 2010