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154
InductiveDataType Systems
, 2002
"... In a previous work ("Abstract Data Type Systems", TCS 173(2), 1997), the leI two authors presented a combined lmbined made of a (strongl normal3zG9 alrmal rewrite system and a typed #calA#Ik enriched by patternmatching definitions folnitio a certain format,calat the "General Schem ..."
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Cited by 751 (21 self)
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In a previous work ("Abstract Data Type Systems", TCS 173(2), 1997), the leI two authors presented a combined lmbined made of a (strongl normal3zG9 alrmal rewrite system and a typed #calA#Ik enriched by patternmatching definitions folnitio a certain format,calat the "General Schema", whichgeneral39I theusual recursor definitions fornatural numbers and simil9 "basic inductive types". This combined lmbined was shown to bestrongl normalIk39f The purpose of this paper is toreformul33 and extend theGeneral Schema in order to make it easil extensibl3 to capture a more general cler of inductive types, cals, "strictly positive", and to ease the strong normalgAg9Ik proof of theresulGGg system. Thisresul provides a computation model for the combination of anal"DAfGI specification language based on abstract data types and of astrongl typed functional language with strictly positive inductive types.
Modeling and Verifying Systems using a Logic of Counter Arithmetic with Lambda Expressions and Uninterpreted Functions
, 2002
"... In this paper, we present the logic of Counter arithmetic with Lambda expressions and Uninterpreted functions (CLU). CLU generalizes the logic of equality with uninterpreted functions (EUF) with constrained lambda expressions, ordering, and successor and predecessor functions. In addition to mod ..."
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Cited by 145 (44 self)
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In this paper, we present the logic of Counter arithmetic with Lambda expressions and Uninterpreted functions (CLU). CLU generalizes the logic of equality with uninterpreted functions (EUF) with constrained lambda expressions, ordering, and successor and predecessor functions. In addition to modeling pipelined processors that EUF has proved useful for, CLU can be used to model many infinitestate systems including those with infinite memories, finite and infinite queues including lossy channels, and networks of identical processes. Even with this richer expressive power, the validity of a CLU formula can be efficiently decided by translating it to a propositional formula, and then using Boolean methods to check validity. We give theoretical and empirical evidence for the efficiency of our decision procedure. We also describe verification techniques that we have used on a variety of systems, including an outoforder execution unit and the loadstore unit of an industrial microprocessor.
Equations and rewrite rules: a survey
 In Formal Language Theory: Perspectives and Open Problems
, 1980
"... bY ..."
Processor verification using efficient reductions of the logic of uninterpreted functions to propositional logic
 ACM Transactions on Computational Logic
, 1999
"... The logic of equality with uninterpreted functions (EUF) provides a means of abstracting the manipulation of data by a processor when verifying the correctness of its control logic. By reducing formulas in this logic to propositional formulas, we can apply Boolean methods such as Ordered Binary Deci ..."
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Cited by 92 (26 self)
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The logic of equality with uninterpreted functions (EUF) provides a means of abstracting the manipulation of data by a processor when verifying the correctness of its control logic. By reducing formulas in this logic to propositional formulas, we can apply Boolean methods such as Ordered Binary Decision Diagrams (BDDs) and Boolean satisfiability checkers to perform the verification. We can exploit characteristics of the formulas describing the verification conditions to greatly simplify the propositional formulas generated. We identify a class of terms we call "pterms" for which equality comparisons can only be used in monotonically positive formulas. By applying suitable abstractions to the hardware model, we can express the functionality of data values and instruction addresses flowing through an instruction pipeline with pterms. A decision procedure can exploit the restricted uses of pterms by considering only "maximally diverse" interpretations of the associated function symbols...
Ontological Semantics
, 2004
"... This book introduces ontological semantics, a comprehensive approach to the treatment of text meaning by computer. Ontological semantics is an integrated complex of theories, methodologies, descriptions and implementations. In ontological semantics, a theory is viewed as a set of statements determin ..."
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Cited by 90 (28 self)
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This book introduces ontological semantics, a comprehensive approach to the treatment of text meaning by computer. Ontological semantics is an integrated complex of theories, methodologies, descriptions and implementations. In ontological semantics, a theory is viewed as a set of statements determining the format of descriptions of the phenomena with which the theory deals. A theory is associated with a methodology used to obtain the descriptions. Implementations are computer systems that use the descriptions to solve specific problems in text processing. Implementations of ontological semantics are combined with other processing systems to produce applications, such as information extraction or machine translation. The theory of ontological semantics is built as a society of microtheories covering such diverse ground as specific language phenomena, world knowledge organization, processing heuristics and issues relating to knowledge representation and implementation system architecture. The theory briefly sketched above is a toplevel microtheory, the ontological semantics theory per se. Descriptions in ontological semantics include text meaning representations, lexical entries, ontological concepts and instances as well as procedures for manipulating texts and their meanings. Methodologies in ontological semantics are sets of techniques and instructions for acquiring and
Effective Use of Boolean Satisfiability Procedures in the Formal Verification of Superscalar and VLIW Microprocessors
 Journal of Symbolic Computation
, 2001
"... We compare SATcheckers and decision diagrams on the evaluation of Boolean formulas produced in the formal verification of both correct and buggy versions of superscalar and VLIW microprocessors. We identify one SATchecker that significantly outperforms the rest. We evaluate ways to enhance its per ..."
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Cited by 88 (13 self)
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We compare SATcheckers and decision diagrams on the evaluation of Boolean formulas produced in the formal verification of both correct and buggy versions of superscalar and VLIW microprocessors. We identify one SATchecker that significantly outperforms the rest. We evaluate ways to enhance its performance by variations in the generation of the Boolean correctness formulas. We reassess optimizations previously used to speed up the formal verification and probe future challenges.
Lazy Satisfiability Modulo Theories
 Journal on Satisfiability, Boolean Modeling and Computation
, 2007
"... Satisfiability Modulo Theories (SMT) is the problem of deciding the satisfiability of a firstorder formula with respect to some decidable firstorder theory T (SMT (T)). These problems are typically not handled adequately by standard automated theorem provers. SMT is being recognized as increasingl ..."
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Cited by 85 (34 self)
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Satisfiability Modulo Theories (SMT) is the problem of deciding the satisfiability of a firstorder formula with respect to some decidable firstorder theory T (SMT (T)). These problems are typically not handled adequately by standard automated theorem provers. SMT is being recognized as increasingly important due to its applications in many domains in different communities, in particular in formal verification. An amount of papers with novel and very efficient techniques for SMT has been published in the last years, and some very efficient SMT tools are now available. Typical SMT (T) problems require testing the satisfiability of formulas which are Boolean combinations of atomic propositions and atomic expressions in T, so that heavy Boolean reasoning must be efficiently combined with expressive theoryspecific reasoning. The dominating approach to SMT (T), called lazy approach, is based on the integration of a SAT solver and of a decision procedure able to handle sets of atomic constraints in T (Tsolver), handling respectively the Boolean and the theoryspecific components of reasoning. Unfortunately, neither the problem of building an efficient SMT solver, nor even that of acquiring a comprehensive background knowledge in lazy SMT, is of simple solution. In this paper we present an extensive survey of SMT, with particular focus on the lazy approach. We survey, classify and analyze from a theoryindependent perspective the most effective techniques and optimizations which are of interest for lazy SMT and which have been proposed in various communities; we discuss their relative benefits and drawbacks; we provide some guidelines about their choice and usage; we also analyze the features for SAT solvers and Tsolvers which make them more suitable for an integration. The ultimate goals of this paper are to become a source of a common background knowledge and terminology for students and researchers in different areas, to provide a reference guide for developers of SMT tools, and to stimulate the crossfertilization of techniques and ideas among different communities.
Set Constraints are the Monadic Class
, 1992
"... We investigate the relationship between set constraints and the monadic class of firstorder formulas and show that set constraints are essentially equivalent to the monadic class. From this equivalence we can infer that the satisfiability problem for set constraints is complete for NEXPTIME. Mor ..."
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Cited by 70 (0 self)
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We investigate the relationship between set constraints and the monadic class of firstorder formulas and show that set constraints are essentially equivalent to the monadic class. From this equivalence we can infer that the satisfiability problem for set constraints is complete for NEXPTIME. More precisely, we prove that this problem has a lower bound of NTIME(c n= log n ). The relationship between set constraints and the monadic class also gives us decidability and complexity results for certain practically useful extensions of set constraints, in particular "negative projections" and subterm equality tests.
BDD Based Procedures for a Theory of Equality with Uninterpreted Functions
"... . The logic of equality with uninterpreted functions has been proposed for verifying abstract hardware designs. The ability to perform fast satisfiability checking over this logic is imperative for this verification paradigm to be successful. We present symbolic methods for satisfiability checking f ..."
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Cited by 61 (4 self)
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. The logic of equality with uninterpreted functions has been proposed for verifying abstract hardware designs. The ability to perform fast satisfiability checking over this logic is imperative for this verification paradigm to be successful. We present symbolic methods for satisfiability checking for this logic. The first procedure is based on restricting analysis to finite instantiations of the design. The second procedure directly reasons about equality by introducing Booleanvalued indicator variables for equality. Theoretical and experimental evidence shows the superiority of the second approach. 1 Verifying Highlevel Designs Using the Theory of Equality A common problem with automatic formal verification is that the computational resources required for verification increase rapidly with the size of the design. Stateof the art tools for verification of gatelevel designs are not capable of routinely verifying designs possessing more than a hundred to two hundred binaryvalued l...
Safety and translation of relational calculus queries
 ACM Transactions on Database Systems
, 1991
"... Notallqueries inrelational calculus can beanswered sensibly when disjunction, negation, and universal quantification are allowed, The class of relation calculus queries or formulas that have sensible answers is called the domam independent class which is known to be undecidable. Subsequent research ..."
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Cited by 60 (0 self)
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Notallqueries inrelational calculus can beanswered sensibly when disjunction, negation, and universal quantification are allowed, The class of relation calculus queries or formulas that have sensible answers is called the domam independent class which is known to be undecidable. Subsequent research has focused on identifying large decidable subclasses of domain independent formulas. In this paper we investigate the properties of two such classes: the et,aluable formulas and the allowed formulas. Although both classes have been defined before, we give simplified definitions, present short proofs of their main properties, and describe a method to incorporate equality. Although evaluable queries have sensible answers, it is not straightforward to compute them efficiently or correctly, We introduce relational algebra normal form for formulas from which form the correct translation into relational algebra istrivlal. We give algorithms to transform anevaluable formula into an equivalent allowed formula and from there into relational algebra normal form, Our algorithms avoid use of the socalled Dom relation, consisting of all constants appearing in the database or the query. Finally, we describe a restriction under which every domain independent formula is evaluable