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DISCOUNT  A distributed and learning equational prover
 JOURNAL OF AUTOMATED REASONING
, 1996
"... The DISCOUNT system is a distributed equational theorem prover based on the teamwork method for knowledgebased distribution. It uses an extended version of unfailing KnuthBendix completion that is able to deal with arbitrarily quantified goals. DISCOUNT features many different control strategies t ..."
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Cited by 31 (16 self)
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The DISCOUNT system is a distributed equational theorem prover based on the teamwork method for knowledgebased distribution. It uses an extended version of unfailing KnuthBendix completion that is able to deal with arbitrarily quantified goals. DISCOUNT features many different control strategies that cooperate using the teamwork approach. Competition between multiple strategies, combined with reactive planning, results in an adaptation of the whole system to given problems, and thus in a very high degree of independence from user interaction. Teamwork also provides a suitable framework for the use of control strategies based on learning from previous proof experiences. One of these strategies forms the core of the expert global learn, which is capable of learning from successful proofs of several problems. This expert, running sequentially, was one of the entrants in the competition (DISCOUNT/GL), while a distributed DISCOUNT system running on two workstations was another entrant....
On Using Ground Joinable Equations in Equational Theorem Proving
 PROC. OF THE 3RD FTP, ST. ANDREWS, SCOTTLAND, FACHBERICHTE INFORMATIK. UNIVERSITAT KOBLENZLANDAU
, 2000
"... When rewriting and completion techniques are used for equational theorem proving, the axiom set is saturated with the aim to get a rewrite system that is terminating and confluent on ground terms. To reduce the computational effort it should (1) be powerful for rewriting and (2) create not too ma ..."
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Cited by 11 (2 self)
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When rewriting and completion techniques are used for equational theorem proving, the axiom set is saturated with the aim to get a rewrite system that is terminating and confluent on ground terms. To reduce the computational effort it should (1) be powerful for rewriting and (2) create not too many critical pairs. These problems become especially important if some operators are associative and commutative (AC ). We show in this paper how these two goals can be reached to some extent by using ground joinable equations for simplification purposes and omitting them from the generation of new facts. For the special case of AC operators we present a simple redundancy criterion which is easy to implement, efficient, and effective in practice, leading to significant speedups.
KnuthBendix constraint solving is NPcomplete
 IN PROCEEDINGS OF 28TH INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING (ICALP), VOLUME 2076 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2000
"... We show that the problem of solving KnuthBendix ordering constraints is NPcomplete, as a corollary we show that the existential firstorder theory of any term algebra with the KnuthBendix ordering is NPcomplete. ..."
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Cited by 11 (2 self)
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We show that the problem of solving KnuthBendix ordering constraints is NPcomplete, as a corollary we show that the existential firstorder theory of any term algebra with the KnuthBendix ordering is NPcomplete.
Equational Prover of Theorema
, 2003
"... The equational prover of the Theorema system is described. It is implemented on Mathematica and is designed for unit equalities in the first order or in the applicative higher order form. A (restricted) usage of sequence variables and Mathematica builtin functions is allowed. ..."
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Cited by 7 (6 self)
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The equational prover of the Theorema system is described. It is implemented on Mathematica and is designed for unit equalities in the first order or in the applicative higher order form. A (restricted) usage of sequence variables and Mathematica builtin functions is allowed.
System Description: Waldmeister  Improvements in Performance and Ease of Use
, 1999
"... this paper we present two aspects of our recent work which aim at improving the system with respect to performance and ease of use. Section 2 describes a more powerful hypothesis handling. In Sect. 3 we investigate the control of the proof search and outline our current component of selfadaptation ..."
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Cited by 6 (2 self)
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this paper we present two aspects of our recent work which aim at improving the system with respect to performance and ease of use. Section 2 describes a more powerful hypothesis handling. In Sect. 3 we investigate the control of the proof search and outline our current component of selfadaptation to the given proof problem
G.: Integrating an automated theorem prover into Agda
 NASA Formal Methods (NFM 2011), LNCS
, 2011
"... Abstract. Agda is a dependently typed functional programming language and a proof assistant in which developing programs and proving their correctness is one activity. We show how this process can be enhanced by integrating external automated theorem provers, provide a prototypical integration of th ..."
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Cited by 3 (0 self)
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Abstract. Agda is a dependently typed functional programming language and a proof assistant in which developing programs and proving their correctness is one activity. We show how this process can be enhanced by integrating external automated theorem provers, provide a prototypical integration of the equational theorem prover Waldmeister, and give examples of how this proof automation works in practice. 1
Comparing Unification Algorithms in FirstOrder Theorem Proving
"... Abstract. Unification is one of the key procedures in firstorder theorem provers. Most firstorder theorem provers use the Robinson unification algorithm. Although its complexity is in the worst case exponential, the algorithm is easy to implement and examples where it may show exponential behaviou ..."
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Abstract. Unification is one of the key procedures in firstorder theorem provers. Most firstorder theorem provers use the Robinson unification algorithm. Although its complexity is in the worst case exponential, the algorithm is easy to implement and examples where it may show exponential behaviour are believed to be atypical. More sophisticated algorithms, such as the Martelli and Montanari algorithm, offer polynomial complexity but are harder to implement. Very little is known the practical perfomance of unification algorithms in theorem provers: previous case studies have been conducted on small numbers of artificially chosen problem and compared termtoterm unification while the best theorem provers perform setoftermstoterm unification using term indexing. To evaluate the performance of unification in the context of term indexing, we made largescale experiments over the TPTP library containing thousands of problems using the COMPIT methodology. Our results confirm that the Robinson algorithm is the most efficient one in practice. They also reveal main sources of inefficiency in other algorithms. We present these results and discuss various modification of unification algorithms. 1
Simplifying Pointer Kleene Algebra
"... Pointer Kleene algebra has proved to be a useful abstraction for reasoning about reachability properties and correctly deriving pointer algorithms. Unfortunately it comes with a complex set of operations and defining (in)equations which exacerbates its practicability with automated theorem proving s ..."
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Pointer Kleene algebra has proved to be a useful abstraction for reasoning about reachability properties and correctly deriving pointer algorithms. Unfortunately it comes with a complex set of operations and defining (in)equations which exacerbates its practicability with automated theorem proving systems but also its use by theory developers. Therefore we provide an easier access to this approach by simpler axioms and laws which also are more amenable to automatic theorem proving systems. 1
Learning From Previous Proof Experience: A Survey
, 1999
"... We present an overview of various learning techniques used in automated theorem provers. We characterize the main problems arising in this context and classify the solutions to these problems from published approaches. We analyze the suitability of several combinations of solutions for different app ..."
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We present an overview of various learning techniques used in automated theorem provers. We characterize the main problems arising in this context and classify the solutions to these problems from published approaches. We analyze the suitability of several combinations of solutions for different approaches to theorem proving and place these combinations in a spectrum ranging from provers using very specialized learning approaches to optimally adapt to a small class of proof problems, to provers that learn more general kinds of knowledge, resulting in systems that are less efficient in special cases but show improved performance for a wide range of problems. Finally, we suggest combinations of solutions for various proof philosophies.
Contents
, 2009
"... Huffman’s algorithm is a procedure for constructing a binary tree with minimum weighted path length. This report presents a formal proof of the correctness of Huffman’s algorithm written using Isabelle/HOL. Our proof closely follows the sketches found in standard algorithms textbooks, uncovering a f ..."
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Huffman’s algorithm is a procedure for constructing a binary tree with minimum weighted path length. This report presents a formal proof of the correctness of Huffman’s algorithm written using Isabelle/HOL. Our proof closely follows the sketches found in standard algorithms textbooks, uncovering a few snags in the process. Another distinguishing feature of our formalization is the use of custom induction rules to help Isabelle’s automatic tactics, leading to very short