Abstract not found

In this paper we show how hierarchical reasoning can be used to verify properties of complex systems. Chains of local theory extensions are used to model a case study taken from the European Train Control System (ETCS) standard, but considerably simplified. We show how testing invariants and bounded model checking can automatically be reduced to checking satisfiability of ground formulae over a base theory. 1

Abstract. We present a general framework which allows to identify complex theories important in verification for which efficient reasoning methods exist. The framework we present is based on a general notion of locality. We show that locality considerations allow us to obtain parameterized decidability and complexity results for many (combinations of) theories important in verification in general and in the verification of parametric systems in particular. We give numerous examples; in particular we show that several theories of data structures studied in the verification literature are local extensions of a base theory. The general framework we use allows us to identify situations in which some of the syntactical restrictions imposed in previous papers can be relaxed. 1

We extend existing verification methods for CSP-OZ-DC to reason about real-time systems with complex data types and timing parameters. We show that important properties of systems can be encoded in well-behaved logical theories in which hierarchic reasoning is possible. Thus, testing invariants and bounded model checking can be reduced to checking satisfiability of ground formulae over a simple base theory. We illustrate the ideas by means of a simplified version of a case study from the European Train Control System standard.

Abstract. We present an overview of results on hierarchical and modular reasoning in complex theories. We show that for a special type of extensions of a base theory, which we call local, hierarchic reasoning is possible (i.e. proof tasks in the extension can be hierarchically reduced to proof tasks w.r.t. the base theory). Many theories important for computer science or mathematics fall into this class (typical examples are theories of data structures, theories of free or monotone functions, but also functions occurring in mathematical analysis). In fact, it is often necessary to consider complex extensions, in which various types of functions or data structures need to be taken into account at the same time. We show how such local theory extensions can be identified and under which conditions locality is preserved when combining theories, and we investigate possibilities of efficient modular reasoning in such theory combinations. We present several examples of application domains where local theories and local theory extensions occur in a natural way. We show, in particular, that various phenomena analyzed in the verification literature can be explained in a unified way using the notion of locality. 1

The Knuth-Bendix ordering is usually preferred over the lexicographic path ordering in successful implementations of resolution and superposition calculi. However, it is incompatible with certain requirements of hierarchic superposition calculi, and it also does not allow non-linear definition equations to be oriented in a natural way. We present two extensions of the Knuth-Bendix ordering that make it possible to overcome these restrictions. 1

The topic of this article is decision procedures for satisfiability modulo theories (SMT) of arbitrary quantifier-free formulæ. We propose an approach that decomposes the formula in such a way that its definitional part, including the theory, can be compiled by a rewrite-based firstorder theorem prover, and the residual problem can be decided by an SMT-solver, based on the Davis-Putnam-Logemann-Loveland procedure. The resulting decision by stages mechanism may unite the complementary strengths of first-order provers and SMT-solvers. We demonstrate its practicality by giving decision procedures for the theories of records, integer offsets and arrays, with or without extensionality, and for combinations including such theories.

ATRs (AVACS Technical Reports) are freely downloadable from www.avacs.org Copyright c ○ August 2010 by the author(s)

this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be found at the ENTCS Macro Home Page. Applications of hierarchical reasoning in the verification of complex systems 3

Abstract. In this paper we study possibilities of efficient reasoning in combinations of theories over possibly non-disjoint signatures. We first present a class of theory extensions (called local extensions) in which hierarchical reasoning is possible, and give several examples from computer science and mathematics in which such extensions occur in a natural way. We then identify situations in which combinations of local extensions of a theory are again local extensions of that theory. We thus obtain criteria both for recognizing wider classes of local theory extensions, and for modular reasoning in combinations of theories over non-disjoint signatures. 1