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79
Word Unification and Transformation of Generalized Equations
 Journal of Automated Reasoning
, 1993
"... Makanin's algorithm [Ma77] shows that it is decidable whether a word equation has a solution. The original description was hard to understand and not designed for implementation. Since words represent a fundamental data type, various authors have given improved descriptions [P'e81, Ab87, Sc90, Ja90] ..."
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Cited by 21 (1 self)
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Makanin's algorithm [Ma77] shows that it is decidable whether a word equation has a solution. The original description was hard to understand and not designed for implementation. Since words represent a fundamental data type, various authors have given improved descriptions [P'e81, Ab87, Sc90, Ja90]. In this paper we present a version of the algorithm which probably cannot be further simplified without fundamentally new insights which exceed Makanin's original ideas. We give a transformation which is efficient, conceptually simple and applies to arbitrary generalized equations. No further subprocedure is needed for the generation of the search tree. Particular attention is then given to the proof that proper generalized equations are transformed into proper generalized equations. This point, which is important for the termination argument, was treated erroneously in other papers. We also show that a combination of the basic algorithm for stringunification (see [Pl72, Le72, Si75, Si78]...
Temporal Semantic Assumptions and Their Use in Databases
 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING
, 1998
"... Temporal data explicitly stored in a temporal database are often associated with certain semantic assumptions. Each assumption can be viewed as a way of deriving implicit information from the explicitly stored data. Rather than leaving the task of deriving (possibly in nite) implicit data to applica ..."
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Cited by 18 (2 self)
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Temporal data explicitly stored in a temporal database are often associated with certain semantic assumptions. Each assumption can be viewed as a way of deriving implicit information from the explicitly stored data. Rather than leaving the task of deriving (possibly in nite) implicit data to application programs, as is the case currently, it is desirable that this be handled by the database management systems. To achieve this, this paper formalizes and studies two types of semantic assumptions: pointbased and intervalbased. The pointbased assumptions include those assumptions that use interpolation methods, while the intervalbased assumptions include those that involve different temporal types (time granularities). In order to incorporate semantic assumptions into query evaluation, this paper introduces a translation procedure that converts a user query into a system query such that the answer of this system query over the explicit data is the same as that of the user query over the explicit and the implicit data. The paper also investigates the niteness (safety) of user queries and system queries.
Fluid Updates: Beyond Strong vs. Weak Updates
"... We describe a symbolic heap abstraction that unifies reasoning about arrays, pointers, and scalars, and we define a fluid update operation on this symbolic heap that relaxes the dichotomy between strong and weak updates. Our technique is fully automatic, does not suffer from the kind of statespac ..."
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Cited by 18 (8 self)
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We describe a symbolic heap abstraction that unifies reasoning about arrays, pointers, and scalars, and we define a fluid update operation on this symbolic heap that relaxes the dichotomy between strong and weak updates. Our technique is fully automatic, does not suffer from the kind of statespace explosion problem partitionbased approaches are prone to, and can naturally express properties that hold for noncontiguous array elements. We demonstrate the effectiveness of this technique by evaluating it on challenging array benchmarks and by automatically verifying buffer accesses and dereferences in five Unix Coreutils applications with no annotations or false alarms.
Decision procedures for recursive data structures with integer constraints
 In International Joint Conference on Automated Reasoning, volume 3097 of LNCS
, 2004
"... ..."
Deciding Presburger Arithmetic by Model Checking and Comparisons with Other Methods
 In Proceedings of FMCAD 02
, 2002
"... We present a new way of using Binary Decision Diagrams in automata based algorithms for solving the satisfiability problem of quantifierfree Presburger arithmetic. Unlike in previous approaches [5, 2, 19], we translate the satisfiability problem into a model checking problem and use the existing ..."
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Cited by 16 (1 self)
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We present a new way of using Binary Decision Diagrams in automata based algorithms for solving the satisfiability problem of quantifierfree Presburger arithmetic. Unlike in previous approaches [5, 2, 19], we translate the satisfiability problem into a model checking problem and use the existing BDDbased model checker SMV [13] as our primary engine.
Using The `RCC' Formalism To Describe The Topology Of Spherical Regions
, 1996
"... This research report concerns the topology of 2dimensional regions embedded in spherical surfaces, such as that of the Earth (`spherical regions'). It shows that the RCC (RegionConnection Calculus) firstorder logic formalism for qualitative spatial representation and reasoning is sufficiently exp ..."
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Cited by 13 (2 self)
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This research report concerns the topology of 2dimensional regions embedded in spherical surfaces, such as that of the Earth (`spherical regions'). It shows that the RCC (RegionConnection Calculus) firstorder logic formalism for qualitative spatial representation and reasoning is sufficiently expressive to support a rich topological taxonomy of uniformly twodimensional regions forming parts of a spherical surface such as the Earth's. However, there are potentially useful constraints on the topology of such regions which the language of RCC cannot capture. Furthermore, the spherical model of the RCC axiom set developed here permits the construction of a proof that the theory axiomatised by this axiom set is undecidable (a result also derivable from (Grzegorczyk 1951).
Verifying and reflecting quantifier elimination for Presburger arithmetic
 LOGIC FOR PROGRAMMING, ARTIFICIAL INTELLIGENCE, AND REASONING
, 2005
"... We present an implementation and verification in higherorder logic of Cooper’s quantifier elimination for Presburger arithmetic. Reflection, i.e. the direct execution in ML, yields a speedup of a factor of 200 over an LCFstyle implementation and performs as well as a decision procedure handcode ..."
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Cited by 11 (7 self)
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We present an implementation and verification in higherorder logic of Cooper’s quantifier elimination for Presburger arithmetic. Reflection, i.e. the direct execution in ML, yields a speedup of a factor of 200 over an LCFstyle implementation and performs as well as a decision procedure handcoded in ML.
Term algebras with length function and bounded quantifier alternation
 In Theorem Proving in HigherOrder Logics, volume 3223 of LNCS
, 2004
"... .)L: TA! Z. Formulae are formed from term literals and integerliterals using logical connectives and quantifications. Term literals are exactly ..."
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Cited by 11 (4 self)
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.)L: TA! Z. Formulae are formed from term literals and integerliterals using logical connectives and quantifications. Term literals are exactly
Proving Conditional Termination
"... Abstract. We describe a method for synthesizing reasonable underapproximations to weakest preconditions for termination—a longstanding open problem. The paper provides experimental evidence to demonstrate the usefulness of the new procedure. 1 ..."
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Cited by 11 (3 self)
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Abstract. We describe a method for synthesizing reasonable underapproximations to weakest preconditions for termination—a longstanding open problem. The paper provides experimental evidence to demonstrate the usefulness of the new procedure. 1
A thread of HOL development
 Computer Journal
"... The HOL system is a mechanized proof assistant for higher order logic that has been under continuous development since the mid1980s, by an everchanging group of developers and external contributors. We give a brief overview of various implementations of the HOL logic before focusing on the evoluti ..."
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Cited by 11 (7 self)
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The HOL system is a mechanized proof assistant for higher order logic that has been under continuous development since the mid1980s, by an everchanging group of developers and external contributors. We give a brief overview of various implementations of the HOL logic before focusing on the evolution of certain important features available in a recent implementation. We also illustrate how the module system of Standard ML provided security and modularity in the construction of the HOL kernel, as well as serving in a separate capacity as a useful representation medium for persistent, hierarchical logical theories.