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SCIL  Symbolic Constraints in Integer Linear Programming
, 2002
"... We describe SCIL. SCIL introduces symbolic constraints into branchandcutandprice algorithms for integer linear programs. Symbolic constraints are known from constraint programming and contribute signi cantly to the expressive power, ease of use, and e ciency of constraint programs. ..."
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Cited by 4 (0 self)
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We describe SCIL. SCIL introduces symbolic constraints into branchandcutandprice algorithms for integer linear programs. Symbolic constraints are known from constraint programming and contribute signi cantly to the expressive power, ease of use, and e ciency of constraint programs.
Pumping, Cleaning and Symbolic Constraints Solving
"... We define a new class of tree automata which generalizes both the encompassment automata of [3] and the automata with tests between brothers of [2]. We give a pumping lemma for these automata, which implies that the emptiness of the corresponding language is decidable. Then, we show how to decide e ..."
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Cited by 12 (5 self)
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by induction in equational theories [10, 1], in proving properties of equational specifications [11] and in constraint solving in quotient algebras [9]. Ground reducibility has been shown decidable in the general case by D. Plaisted [15], D. Kapur et al. [11], E. Kounalis [12]. Recently, some of us proved a
On the Combination of Symbolic Constraints, Solution Domains, and Constraint Solvers
 In Proceedings of the First International Conference on Principles and Practice of Constraint Programming
"... When combining languages for symbolic constraints, one is typically faced with the problem of how to treat "mixed" constraints. The two main problems are (1) how to define a combined solution structure over which these constraints are to be solved, and (2) how to combine the constraint sol ..."
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Cited by 26 (3 self)
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When combining languages for symbolic constraints, one is typically faced with the problem of how to treat "mixed" constraints. The two main problems are (1) how to define a combined solution structure over which these constraints are to be solved, and (2) how to combine the constraint
Rewritebased Deduction and Symbolic Constraints
 In Proceedings of the 16th International Conference on Automated Deduction, volume 1632 of LNAI
, 1997
"... Introduction Building a stateoftheart theorem prover requires the combination of at least three main ingredients: good theory, clever heuristics, and the necessary engineering skills to implement it all in an efficient way. Progress in each of these ingredients interacts in different ways. On t ..."
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Cited by 5 (2 self)
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Introduction Building a stateoftheart theorem prover requires the combination of at least three main ingredients: good theory, clever heuristics, and the necessary engineering skills to implement it all in an efficient way. Progress in each of these ingredients interacts in different ways. On the one hand, new theoretical insights replace heuristics by more precise and effective techniques. For example, the completeness proof of basic paramodulation [NR95,BGLS95] shows why no inferences below Skolem functions are needed, as conjectured by McCune in [McC90]. Regarding implementation techniques, adhoc algorithms for procedures like demodulation or subsumption are replaced by efficient, reusable, generalpurpose indexing data structures for which the time and space requirements are wellknown. But, on the other hand, theory also advances in other directions, producing new ideas for which the development of implementation techniques and heuristics that make
Paramodulation with Builtin ACTheories and Symbolic Constraints
 Journal of Symbolic Computation
, 1996
"... this paper we overcome these drawbacks by working with clauses with symbolic constraints (Kirchner et al., 1990; Nieuwenhuis and Rubio, 1992; Rubio, 1994; Nieuwenhuis and Rubio, 1995) . A constrained clause C [[ T ]] is a shorthand for the set of ground instances of the clause part C satisfying the ..."
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Cited by 12 (7 self)
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this paper we overcome these drawbacks by working with clauses with symbolic constraints (Kirchner et al., 1990; Nieuwenhuis and Rubio, 1992; Rubio, 1994; Nieuwenhuis and Rubio, 1995) . A constrained clause C [[ T ]] is a shorthand for the set of ground instances of the clause part C satisfying
The Symbol Grounding Problem
, 1990
"... There has been much discussion recently about the scope and limits of purely symbolic models of the mind and about the proper role of connectionism in cognitive modeling. This paper describes the "symbol grounding problem": How can the semantic interpretation of a formal symbol system be m ..."
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Cited by 1072 (18 self)
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There has been much discussion recently about the scope and limits of purely symbolic models of the mind and about the proper role of connectionism in cognitive modeling. This paper describes the "symbol grounding problem": How can the semantic interpretation of a formal symbol system
Constraint Networks
, 1992
"... Constraintbased reasoning is a paradigm for formulating knowledge as a set of constraints without specifying the method by which these constraints are to be satisfied. A variety of techniques have been developed for finding partial or complete solutions for different kinds of constraint expression ..."
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Cited by 1149 (43 self)
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Constraintbased reasoning is a paradigm for formulating knowledge as a set of constraints without specifying the method by which these constraints are to be satisfied. A variety of techniques have been developed for finding partial or complete solutions for different kinds of constraint
Symbolic Model Checking without BDDs
, 1999
"... Symbolic Model Checking [3, 14] has proven to be a powerful technique for the verification of reactive systems. BDDs [2] have traditionally been used as a symbolic representation of the system. In this paper we show how boolean decision procedures, like Stalmarck's Method [16] or the Davis ..."
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Cited by 910 (74 self)
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Symbolic Model Checking [3, 14] has proven to be a powerful technique for the verification of reactive systems. BDDs [2] have traditionally been used as a symbolic representation of the system. In this paper we show how boolean decision procedures, like Stalmarck's Method [16] or the Davis
Symbolic Constraints in Constructive Geometric Constraint Solving
, 1997
"... In design and manufacturing applications, users of computer aided design systems want to define relationships between dimension variables, since such relationships express design intent very flexibly. This work reports on a technique developed to enhance a class of constructive geometric constraint ..."
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Cited by 19 (5 self)
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In design and manufacturing applications, users of computer aided design systems want to define relationships between dimension variables, since such relationships express design intent very flexibly. This work reports on a technique developed to enhance a class of constructive geometric constraint
The Semantics Of Constraint Logic Programs
 JOURNAL OF LOGIC PROGRAMMING
, 1996
"... This paper presents for the first time the semantic foundations of CLP in a selfcontained and complete package. The main contributions are threefold. First, we extend the original conference paper by presenting definitions and basic semantic constructs from first principles, giving new and comp ..."
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Cited by 872 (14 self)
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and complete proofs for the main lemmas. Importantly, we clarify which theorems depend on conditions such as solution compactness, satisfaction completeness and independence of constraints. Second, we generalize the original results to allow for incompleteness of the constraint solver. This is important
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