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18
Hierarchic reasoning in local theory extensions
 20th International Conference on Automated Deduction (CADE20), LNAI 3632
, 2005
"... Abstract. We show that for special types of extensions of a base theory, which we call local, efficient hierarchic reasoning is possible. We identify situations in which it is possible, for an extension T1 of a theory T0, to express the decidability and complexity of the universal theory of T1 in te ..."
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Cited by 40 (19 self)
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Abstract. We show that for special types of extensions of a base theory, which we call local, efficient hierarchic reasoning is possible. We identify situations in which it is possible, for an extension T1 of a theory T0, to express the decidability and complexity of the universal theory of T1 in terms of the decidability resp. complexity of suitable fragments of the theory T0 (universal or ∀∃). These results apply to theories related to data types, but also to certain theories of functions from mathematics. 1
On local reasoning in verification
 In TACAS
, 2008
"... 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 decidabil ..."
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Cited by 21 (9 self)
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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
Applications of hierarchical reasoning in the verification of complex systems
 Electronic Notes in Computer Science
, 2006
"... 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 ..."
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Cited by 17 (13 self)
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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
Hierarchical and modular reasoning in complex theories: The case of local theory extensions
 In Proc. 6th Int. Symp. Frontiers of Combining Systems (FroCos 2007), LNCS 4720
, 2007
"... 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 ..."
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Cited by 11 (7 self)
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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
Verifying CSPOZDC specifications with complex data types and timing parameters
 IN: IFM. VOLUME 4519 OF LNCS. (2007) TO
, 2007
"... We extend existing verification methods for CSPOZDC to reason about realtime systems with complex data types and timing parameters. We show that important properties of systems can be encoded in wellbehaved logical theories in which hierarchic reasoning is possible. Thus, testing invariants and ..."
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Cited by 10 (8 self)
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We extend existing verification methods for CSPOZDC to reason about realtime systems with complex data types and timing parameters. We show that important properties of systems can be encoded in wellbehaved 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.
Extensions of the KnuthBendix ordering with LPOlike properties
, 2007
"... The KnuthBendix 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 nonlinear definition equat ..."
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Cited by 6 (0 self)
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The KnuthBendix 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 nonlinear definition equations to be oriented in a natural way. We present two extensions of the KnuthBendix ordering that make it possible to overcome these restrictions. 1
Theory decision by decomposition
, 2008
"... The topic of this article is decision procedures for satisfiability modulo theories (SMT) of arbitrary quantifierfree 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 rewritebased firstorder theorem pro ..."
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Cited by 3 (2 self)
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The topic of this article is decision procedures for satisfiability modulo theories (SMT) of arbitrary quantifierfree 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 rewritebased firstorder theorem prover, and the residual problem can be decided by an SMTsolver, based on the DavisPutnamLogemannLoveland procedure. The resulting decision by stages mechanism may unite the complementary strengths of firstorder provers and SMTsolvers. 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.
ISSN: 18609821Publisher: Sonderforschungsbereich/Transregio 14 AVACS (Automatic Verification and Analysis of Complex Systems)
, 2010
"... ATRs (AVACS Technical Reports) are freely downloadable from www.avacs.org Copyright c ○ August 2010 by the author(s) ..."
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ATRs (AVACS Technical Reports) are freely downloadable from www.avacs.org Copyright c ○ August 2010 by the author(s)