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Model checking with multi-valued logics
, 2003
"... Abstract. In multi-valued model checking, a temporal logic formula is interpreted relative to a structure not as a truth value but as a lattice element. In this paper we present new algorithms for multi-valued model checking. We first show how to reduce multi-valued model checking with any distribut ..."
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Abstract. In multi-valued model checking, a temporal logic formula is interpreted relative to a structure not as a truth value but as a lattice element. In this paper we present new algorithms for multi-valued model checking. We first show how to reduce multi-valued model checking with any distributive DeMorgan lattice to standard, two-valued model check-ing. We then present a direct, automata-theoretic algorithm for multi-valued model checking with logics as expressive as the modal mu-calculus. As part of showing correctness of the algorithm, we present a new fun-damental result about extended alternating automata, a generalization of standard alternating automata. 1
A domain equation for refinement of partial systems
- UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENC
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CTL Model-Checking over Logics with Non-Classical Negations
- PROC. OF 33RD IEEE INT. SYMP. ON MULTI-VALUED LOGICS (ISMVL’03
, 2003
"... In earlier work [9], we defined CTL model-checking over finite-valued logics with De Morgan negation. In this paper, we extend this work to logics with intuitionistic, Galois and minimal negations, calling the resulting language CTL. We define CTL operators and show that they can be computed using ..."
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Cited by 9 (1 self)
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In earlier work [9], we defined CTL model-checking over finite-valued logics with De Morgan negation. In this paper, we extend this work to logics with intuitionistic, Galois and minimal negations, calling the resulting language CTL. We define CTL operators and show that they can be computed using fixpoints. We further discuss how to extend our existing multi-valued model-checker Chek [8] to reasoning over these logics.
Multi-valued model checking games
- In Proc. 3rd ATVA, LNCS 3707
, 2005
"... Abstract. This work extends the game-based framework of µ-calculus model checking to the multi-valued setting. In multi-valued model checking a formula is interpreted over a Kripke structure defined over a lattice. The value of the formula is also an element of the lattice. We define a new game for ..."
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Cited by 7 (1 self)
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Abstract. This work extends the game-based framework of µ-calculus model checking to the multi-valued setting. In multi-valued model checking a formula is interpreted over a Kripke structure defined over a lattice. The value of the formula is also an element of the lattice. We define a new game for this problem and derive from it a direct model checking algorithm that handles the multi-valued structure without any reduction. We investigate the properties of the new game, both independently, and in comparison to the automata-based approach. We show that the usual resemblance between the two approaches does not hold in the multivalued setting and show how it can be regained by changing the nature of the game. 1
Consistent partial model checking
- Electronic Notes in Theoretical Computer Science
, 2004
"... We propose assertion-consistency (AC) semi-lattices as suitable orders for the analysis of partial models. Such orders express semantic entailment, multiple-viewpoint and multiple-valued analysis, maintain internal consistency of reasoning, and subsume finite De Morgan lattices. We classify those or ..."
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Cited by 6 (1 self)
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We propose assertion-consistency (AC) semi-lattices as suitable orders for the analysis of partial models. Such orders express semantic entailment, multiple-viewpoint and multiple-valued analysis, maintain internal consistency of reasoning, and subsume finite De Morgan lattices. We classify those orders that are finite and distributive and apply them to design an efficient algorithm for multiple-viewpoint checking, where checks are delegated to single-viewpoint models — efficiently driven by the order structure. Instrumentations of this algorithm enable the detection and location of inconsistencies across viewpoint boundaries. To validate the approach, we investigate multiple-valued models and their compositional property semantics over a finite distributive AC lattice. We prove that this semantics is computed by our algorithm above whenever the primes of the AC lattice determine ‘projected’ single viewpoints and the order between primes is preserved as refinements of single-viewpoint models. As a case study, we discuss a multiple-valued notion of state-machines with first-order logic plus transitive closure. 1
A Framework For Compositional Verification of Multi-Valued Systems Via Abstraction-Refinement
, 2009
"... We present a framework for fully automated compositional verification of µ-calculus specifications over multi-valued systems, based on multivalued abstraction and refinement. Multi-valued models are widely used in many applications of model checking. They enable a more precise modeling of systems b ..."
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We present a framework for fully automated compositional verification of µ-calculus specifications over multi-valued systems, based on multivalued abstraction and refinement. Multi-valued models are widely used in many applications of model checking. They enable a more precise modeling of systems by distinguishing several levels of uncertainty and inconsistency. Successful verification tools such as STE (for hardware) and YASM (for software) are based on multi-valued models. Our compositional approach model checks individual components of a system. Only if all individual checks return indefinite values, the parts of the components which are responsible for these values, are composed and checked. Thus the construction of the full system is avoided. If the latter check is still indefinite, then a refinement is needed. We formalize our framework based on bilattices, consisting of a truth lattice and an information lattice. Formulas interpreted over a multi-valued model are evaluated w.r.t. to the truth lattice. On the other hand, refinement is now aimed at increasing the information level of model details, thus also increasing the information level of the model checking result. Based on the two lattices, we suggest how multi-valued models should be composed, checked, and refined.
DOI: 10.1017/S0960129504004268 Printed in the United Kingdom A domain equation for refinement of partial systems
, 2002
"... A reactive system can be specified by a labelled transition system, which indicates static structure, along with temporal-logic formulas, which assert dynamic behaviour. But refining the former while preserving the latter can be difficult, because: (i) Labelled transition systems are ‘total ’ – cha ..."
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A reactive system can be specified by a labelled transition system, which indicates static structure, along with temporal-logic formulas, which assert dynamic behaviour. But refining the former while preserving the latter can be difficult, because: (i) Labelled transition systems are ‘total ’ – characterised up to bisimulation – meaning that no new transition structure can appear in a refinement. (ii) Alternatively, a refinement criterion not based on bisimulation might generate a refined transition system that violates the temporal properties. In response, Larsen and Thomson proposed modal transition systems, which are ‘partial’, and defined a refinement criterion that preserved formulas in Hennessy–Milner logic. We show that modal transition systems are, up to a saturation condition, exactly the mixed transition systems of Dams that meet a mix condition, and we extend such systems to non-flat state sets. We then solve a domain equation over the mixed powerdomain whose solution is a bifinite domain that is universal for all saturated modal transition systems and is itself fully abstract when considered as a modal transition system. We demonstrate that many frameworks of partial systems can be translated into the domain: partial Kripke structures, partial bisimulation structures, Kripke modal transition systems, and pointer-shape-analysis graphs. 1.
