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79
Semantical considerations on FloydHoare Logic
, 1976
"... This paper deals with logics of programs. The objective is to formalize a notion of program description, and to give both plausible (semantic) and effective (syntactic) criteria for the notion of truth of a description. A novel feature of this treatment is the development of the mathematics underlyi ..."
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Cited by 212 (10 self)
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This paper deals with logics of programs. The objective is to formalize a notion of program description, and to give both plausible (semantic) and effective (syntactic) criteria for the notion of truth of a description. A novel feature of this treatment is the development of the mathematics underlying FloydHoare axiom systems independently of such systems. Other directions that such research might take are considered.
Interpolation and SATbased model checking
, 2003
"... Abstract. We consider a fully SATbased method of unbounded symbolic model checking based on computing Craig interpolants. In benchmark studies using a set of large industrial circuit verification instances, this method is greatly more efficient than BDDbased symbolic model checking, and compares f ..."
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Cited by 196 (9 self)
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Abstract. We consider a fully SATbased method of unbounded symbolic model checking based on computing Craig interpolants. In benchmark studies using a set of large industrial circuit verification instances, this method is greatly more efficient than BDDbased symbolic model checking, and compares favorably to some recent SATbased model checking methods on positive instances. 1
Lower Bounds for Resolution and Cutting Plane Proofs and Monotone Computations
, 1997
"... We prove an exponential lower bound on the length of cutting plane proofs. The proof uses an extension of a lower bound for monotone circuits to circuits which compute with real numbers and use nondecreasing functions as gates. The latter result is of independent interest, since, in particular, i ..."
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Cited by 135 (5 self)
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We prove an exponential lower bound on the length of cutting plane proofs. The proof uses an extension of a lower bound for monotone circuits to circuits which compute with real numbers and use nondecreasing functions as gates. The latter result is of independent interest, since, in particular, it implies an exponential lower bound for some arithmetic circuits.
Interpolation Theorems, Lower Bounds for Proof Systems, and Independence Results for Bounded Arithmetic
"... A proof of the (propositional) Craig interpolation theorem for cutfree sequent calculus yields that a sequent with a cutfree proof (or with a proof with cutformulas of restricted form; in particular, with only analytic cuts) with k inferences has an interpolant whose circuitsize is at most k. We ..."
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Cited by 86 (2 self)
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A proof of the (propositional) Craig interpolation theorem for cutfree sequent calculus yields that a sequent with a cutfree proof (or with a proof with cutformulas of restricted form; in particular, with only analytic cuts) with k inferences has an interpolant whose circuitsize is at most k. We give a new proof of the interpolation theorem based on a communication complexity approach which allows a similar estimate for a larger class of proofs. We derive from it several corollaries: 1. Feasible interpolation theorems for the following proof systems: (a) resolution. (b) a subsystem of LK corresponding to the bounded arithmetic theory S 2 2 (ff). (c) linear equational calculus. (d) cutting planes. 2. New proofs of the exponential lower bounds (for new formulas) (a) for resolution ([15]). (b) for the cutting planes proof system with coefficients written in unary ([4]). 3. An alternative proof of the independence result of [43] concerning the provability of circuitsize lower bounds ...
Bounded model checking
 Advances in Computers, 58, 2003. i 90] [BCOQ93] [BD91] [Beh03] [BFG+ 91] [BJLY98] [BLL+ 95] [BM83] [Bou02
, 1990
"... Besides Equivalence Checking [KK97, KPKG02] the most important industrial application of SAT is currently Bounded Model Checking (BMC) [BCCZ99]. Both techniques are used for formal hardware verification in the context of electronic design automation (EDA), but have successfully been applied to many ..."
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Cited by 86 (2 self)
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Besides Equivalence Checking [KK97, KPKG02] the most important industrial application of SAT is currently Bounded Model Checking (BMC) [BCCZ99]. Both techniques are used for formal hardware verification in the context of electronic design automation (EDA), but have successfully been applied to many other domains as well. In this chapter, we focus on BMC. In practice, BMC is mainly used for falsification resp. testing, which is concerned with violations of temporal properties. However, the original paper on BMC [BCCZ99] already discussed extensions that can prove properties. A considerable part of this chapter discusses these complete extensions, which are often called “unbounded ” model checking techniques, even though they are build upon the same principles as plain BMC. Two further related applications, in which BMC becomes more and more important, are automatic test case generation for closing coverage holes, and disproving redundancy in designs. Most of the techniques discussed in this chapter transfer to this more general setting as well, even though our focus is on property
PartitionBased Logical Reasoning for FirstOrder and Propositional Theories
 Artificial Intelligence
, 2000
"... In this paper we provide algorithms for reasoning with partitions of related logical axioms in propositional and firstorder logic (FOL). We also provide a greedy algorithm that automatically decomposes a set of logical axioms into partitions. Our motivation is twofold. First, we are concerned with ..."
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Cited by 52 (8 self)
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In this paper we provide algorithms for reasoning with partitions of related logical axioms in propositional and firstorder logic (FOL). We also provide a greedy algorithm that automatically decomposes a set of logical axioms into partitions. Our motivation is twofold. First, we are concerned with how to reason e#ectively with multiple knowledge bases that have overlap in content. Second, we are concerned with improving the e#ciency of reasoning over a set of logical axioms by partitioning the set with respect to some detectable structure, and reasoning over individual partitions. Many of the reasoning procedures we present are based on the idea of passing messages between partitions. We present algorithms for reasoning using forward messagepassing and using backward messagepassing with partitions of logical axioms. Associated with each partition is a reasoning procedure. We characterize a class of reasoning procedures that ensures completeness and soundness of our messagepassing ...
Alternative Semantics for Unawareness
 Games and Economic Behavior
, 2001
"... Modica and Rustichini [1994] provided a logic for reasoning about knowledge where agents may be unaware of certain propositions. However, their original approach had the unpleasant property that nontrivial unawareness was incompatible with partitional information structures. More recently, Modica an ..."
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Cited by 51 (9 self)
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Modica and Rustichini [1994] provided a logic for reasoning about knowledge where agents may be unaware of certain propositions. However, their original approach had the unpleasant property that nontrivial unawareness was incompatible with partitional information structures. More recently, Modica and Rustichini [1999] have provided an approach that allows for nontrivial unawareness in partitional information structures. Here it is shown that their approach can be viewed as a special case of a general approach to unawareness
Logical filtering
 In Proc. IJCAI03
, 2003
"... Filtering denotes any method whereby an agent updates its belief state—its knowledge of the state of the world—from a sequence of actions and observations. In logical filtering, the belief state is a logical formula describing possible world states and the agent has a (possibly nondeterministic) log ..."
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Cited by 38 (7 self)
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Filtering denotes any method whereby an agent updates its belief state—its knowledge of the state of the world—from a sequence of actions and observations. In logical filtering, the belief state is a logical formula describing possible world states and the agent has a (possibly nondeterministic) logical model of its environment and sensors. This paper presents efficient logical filtering algorithms that maintain a compact belief state representation indefinitely, for a broad range of environment classes including nondeterministic, partially observable STRIPS environments and environments in which actions permute the state space. Efficient filtering is also possible when the belief state is represented using prime implicates, or when it is approximated by a logically weaker formula. 1
The software model checker BLAST: Applications to software engineering
 INTERNATIONAL JOURNAL ON SOFTWARE TOOLS TECHNOLOGY TRANSFER
, 2006
"... BLAST is an automatic verification tool for checking temporal safety properties of C programs. Given a C program and a temporal safety property, BLAST either statically proves that the program satisfies the safety property, or provides an execution path that exhibits a violation of the property (or, ..."
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Cited by 34 (5 self)
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BLAST is an automatic verification tool for checking temporal safety properties of C programs. Given a C program and a temporal safety property, BLAST either statically proves that the program satisfies the safety property, or provides an execution path that exhibits a violation of the property (or, since the problem is undecidable, does not terminate). BLAST constructs, explores, and refines abstractions of the program state space based on lazy predicate abstraction and interpolationbased predicate discovery. This paper gives an introduction to BLAST and demonstrates, through two case studies, how it can be applied to program verification and testcase generation. In the first case study, we use BLAST to statically prove memory safety for C programs. We use CCURED, a typebased memorysafety analyzer, to annotate a program with runtime assertions that check for safe memory operations. Then, we use BLAST to remove as many of the runtime checks as possible (by proving that these checks never fail), and to generate execution scenarios that violate the assertions for the remaining runtime checks. In our second case study, we use BLAST to automatically generate test suites that guarantee full coverage with respect to a given predicate. Given a C program and a target predicate p, BLAST determines the program locations q for which there exists a program execution that reaches q with p true, and automatically generates a set of test vectors that generate such executions. Our experiments show that BLAST can provide automated, precise, and scalable analysis for C programs.
Theorem proving with structured theories (full report
, 2001
"... Motivated by the problem of query answering over multiple structured commonsense theories, we exploit graphbased techniques to improve the efficiency of theorem proving for structured theories. Theories are organized into subtheories that are minimally connected by the literals they share. We prese ..."
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Cited by 26 (5 self)
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Motivated by the problem of query answering over multiple structured commonsense theories, we exploit graphbased techniques to improve the efficiency of theorem proving for structured theories. Theories are organized into subtheories that are minimally connected by the literals they share. We present messagepassing algorithms that reason over these theories using consequence finding, specializing our algorithms for the case of firstorder resolution, and for batch and concurrent theorem proving. We provide an algorithm that restricts the interaction between subtheories by exploiting the polarity of literals. We attempt to minimize the reasoning within each individual partition by exploiting existing algorithms for focused incremental and general consequence finding. Finally, we propose an algorithm that compiles each subtheory into one in a reduced sublanguage. We have proven the soundness and completeness of all of these algorithms. 1