Greg Nelson. Combining satisfiability procedures by equality-sharing. In W. W. Bledsoe and D. W. Loveland, editors, Automated Theorem Proving: After 25 Years, volume 29 of Contemporary Mathematics, pages 201--211. American Mathematical Society, Providence, RI, 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....expression, however, arise naturally in many classes of applications. An example of a constraint with mixed terms in the theory of lists and natural numbers is v= 9) y head(y) z where : is the list constructor and head returns the first element of a list. An example, adapted from [12], in the theory of finite trees and real numbers, is f(f( f(y) # i(z) y . Proper instances of CLP(X) cannot deal with these types of constraints sim ply because the CLP computational paradigm does not consider them. In the rest of this paper, we will show a method for extending the CLP ....

Grey Nelson. Combining satisfiability procedures by equality-sharing. Contemporary Mathematics, 29:201-211, 1984.

....is the list constructor and first returns the first element of a list) is a very natural one. Similar claims can be made about constraints such as f(f(x) f(z) y z (where , are arithmetic symbols, and f is an uninterpreted symbol) which often appear in program verification [Nel84] These types of constraints cannot be dealt with by the present CLP systems, simply because their computational paradigm does not consider them. For a perhaps more poignant example of this shortcoming of the CLP scheme, consider a CLP(X 1 , X n ) solver with two constraint domains, 2 and ....

....the constraint structure generated by a suitable combination of all the i s. 3 Combining Satisfiability Procedures We start with a brief review of the model theoretic properties of the NelsonOppen combination method. For a description of the original combination procedure, refer to [NO79] or [Nel84] These properties have been used to prove that the Nelson Oppen method is sound and complete for a certain class of component theories. A formula is in simple conjunctive normal form if it is a conjunction of literals , that is, a conjunction of atomic and negated atomic formulas. Given a ....

[Article contains additional citation context not shown here]

Greg Nelson. Combining satisfiability procedures by equality sharing. Contemporary Mathematics, 29:201--211, 1984.

....produce as verification conditions, is entirely automatic, outputs counterexample contexts, and usually performs well. We have used the same theorem prover for both ESC Modula 3 and ESC Java. The theorem prover Simplify is based on the Nelson Oppen algorithm for cooperating decision procedures [30, 31]. Simplify s decision procedures include an Egraph for the theory of equality including congruence closure, a simplex solver for linear arithmetic, a backtracking search for disjunctions, a matcher for universally quantified formulas, and an ordering theory procedure for various partial orders. ....

Greg Nelson. Combining satisfiability procedures by equality-sharing. In W. W. Bledsoe and D. W. Loveland, editors, Automated Theorem Proving: After 25 Years, volume 29 of Contemporary Mathematics, pages 201--211. American Mathematical Society, 1984.

....in eliciting axioms from a domain expert. Instead of using a theorem prover to answer questions when searching the hierarchy, the domain expert would be used as an oracle to construct portions of a domain theory by traversing the same hierarchy. In previous work on DRAT, the work reported in [7] was extended to show that DRAT s attachment of literal satisfiability procedures to a theorem prover was sound and complete. These results must be extended to DSDRAT and we are considering the framework reported in [2] The extension of DRAT s classification procedure to DSDRAT s classification ....

G. Nelson, "Combining Satisfiability Procedures by Equality Sharing," in Automated Theorem Proving after 25 Years, Bledsoe and Loveland (Eds), American Mathematical Society, 1984.

....and first returns the first element of a list) is a very natural one. Similar claims can be made about constraints such as f(f(x) f(y) #= f(z) # y z # x (where , and # are arithmetic symbols, and f is an uninterpreted symbol) which often appear in program verification [Nel84] These types of constraints cannot be dealt with by the present CLP systems, simply because their computational paradigm does not consider them. For a perhaps more poignant example of this shortcoming of the CLP scheme, consider a CLP(X 1 , X n ) solver with two constraint domains, X ....

....the constraint structure generated by a suitable combination of all the X i s. 3 Combining Satisfiability Procedures We start with a brief review of the model theoretic properties of the NelsonOppen combination method. For a description of the original combination procedure, refer to [NO79] or [Nel84] These properties have been used to prove that the Nelson Oppen method is sound and complete for a certain class of component theories. A formula is in simple conjunctive normal form if it is a conjunction of literals , that is, a conjunction of atomic and negated atomic formulas. Given a ....

[Article contains additional citation context not shown here]

Greg Nelson. Combining satisfiability procedures by equality sharing. <F4.865e+05> Contemporary<F5.317e+05> Mathematics, 29:201--211, 1984.

....list constructor and first returns the first element of a list) is a very natural one. Similar claims can be made about constraints like f(f(x) Gamma f(y) 6= f(z) y z x (where ; Gamma; are arithmetic symbols and f is an uninterpreted symbol) which often appear in program verification [Nel84] These types of constraints cannot be dealt with by the present CLP systems simply because their computational paradigm does not consider them. For a perhaps more poignant example of this shortcoming of the CLP scheme, consider a CLP(X 1 ; X n ) solver with two constraint domains X 1 ; ....

....the constraint structure generated by a suitable combination of all the X i s. 3 Combining Satisfiability Procedures We start with a brief review of the model theoretic properties of the NelsonOppen combination method. For a description of the original combination procedure refer to [NO79] or [Nel84] These properties have been used to prove the that the Nelson Oppen method is sound and complete for a certain class of component theories. A formula is in simple Conjunctive Normal Form if it is a conjunction of literals, that is, a conjunction of atomic and negated atomic formulas. Given a ....

[Article contains additional citation context not shown here]

Greg Nelson. Combining satisfiability procedures by equalitysharing. Contemporary Mathematics, 29:201--211, 1984.

....is only defined for infinite interpretations of the formula itself. 15 Second, it shows that equality propagation between the 15 It looks like the authors had not realized this initially. As a matter of fact, the proofs given in [17] were incorrect. In later papers on the methods, 18] and [16], the problem A New Correctness Proof of the Nelson Oppen Combination Procedure 15 satisfiability procedures of the component theories, the main idea of the method, can be confined to a restricted set of variables. Another contribution of the paper was a characterization of the consistency of ....

Greg Nelson. Combining satisfiability procedures by equality-sharing. Contemporary Mathematics, 29:201--211, 1984.

....is built independently of Nelson and Oppen s results, which in fact can be given as corollaries of ours, and so we will not describe their approach here. The reader interested in a description of the original Nelson Oppen method is referred instead to the original paper [NO79] and its sequels [Nel84, Opp80] 1.3 Paper Outline The paper is organized as follows. In Section 2, we introduce a number of key concepts and lemmas that we will be using in the paper. While the concepts in this section are essential to understanding the rest of the paper, the various results in Section 2.2 should be ....

Greg Nelson. Combining satisfiability procedures by equality-sharing. Contemporary Mathematics, 29:201--211, 1984.

....assignments of the two tasks so that no one is committed to both of them. It turns out that for two separately maintained classes of linear constraints, equality propagation is sufficient: if every equality is propagated cross the boundary, then the two classes have the highest level of consistency[13]. An incremental version of the simplex algorithm is incorporated into the system for linear constraint maintenance[12] which handles the deduction of attribute values and equalities and the retraction of constraint propagation, in addition to satisfiability checking. Every linear constraint is ....

Nelson, G., "Combining Satisfiability Procedures by Equality-Sharing"; Contemporary Mathematics 29, 1984, 201-211.

....however, arise naturally in many classes of applications. An example of a constraint with mixed terms in the theory of lists and natural numbers is v = x 9) y head(y) z u where : is the list constructor and head returns the first element of a list. An example, adapted from [12], in the theory of finite trees and real numbers, is f(f(x) Gamma f(y) 6= f(z) y z x : Proper instances of CLP(X ) cannot deal with these types of constraints simply because the CLP computational paradigm does not consider them. In the rest of this paper, we will show a method for ....

Greg Nelson. Combining satisfiability procedures by equality-sharing. Contemporary Mathematics, 29:201--211, 1984.

....benefit that existing proof procedures need not be modified. However, if partial functions were allowed in the logic, some important proof techniques might not work. For example, totality of uninterpreted function symbols is assumed in the Nelson Oppen method for combining decision procedures [30]. In applications that truly need partial functions, our methodology, as explained in section 4.3, allows further instances of reuse. Our experience in proving facts about sequences has shown that many proof obligations in the mixed HOL HOLCF setting can be broken down into pure HOL propositions. ....

Greg Nelson. Combining satisfiability procedures by equality-sharing. Contemporary Mathematics, 29(1):25--43, 1984.

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Greg Nelson. Combining satisfiability procedures by equality-sharing. In W. W. Bledsoe and D. W. Loveland, editors, Automated Theorem Proving: After 25 Years, volume 29 of Contemporary Mathematics, pages 201--211. American Mathematical Society, Providence, RI, 1984.

No context found.

Greg Nelson. Combining satisfiability procedures by equality-sharing. In W. W. Bledsoe and D. W. Loveland, editors, Automated Theorem Proving: After 25 Years, volume 29 of Contemporary Mathematics, pages 201--211. American Mathematical Society, Providence, RI, 1984.

No context found.

Greg Nelson. Combining satisfiability procedures by equality sharing. In W. W. Bledsoe and D. W. Loveland, editors, Automated Theorem Proving: After 25 Years, volume 29 of Contemporary Mathematics, pages 201--211. American Mathematical Society, 1984.

No context found.

G. Nelson. Combining satisfiability procedures by equality-sharing. In W. W. Bledsoe and D. W. Loveland, editors, Automated Theorem Proving: After 25 Years, volume 29 of Contemporary Mathematics, pages 201--211. American Mathematical Society, Providence, RI, 1984.

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