DISCOUNT: A system for distributed equational deduction

Avenhaus, Jürgen; Denzinger, Jörg; Fuchs, Matthias

doi:10.1007/3-540-59200-8_72

Cited by 32 publications

(17 citation statements)

References 4 publications

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“…We created two different instrumentations of the development version of the Vampire prover, which used the DISCOUNT [2] saturation algorithm. The first instrumentation recorded operations on the unification index of selected literals of active clauses (the resolution index).…”

Section: Benchmarking Methodologymentioning

confidence: 99%

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Comparing Unification Algorithms in First-Order Theorem Proving

Hoder

Воронков

2009

KI 2009: Advances in Artificial Intelligence

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Abstract. Unification is one of the key procedures in first-order theorem provers. Most first-order 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 term-to-term unification while the best theorem provers perform set-of-terms-to-term unification using term indexing. To evaluate the performance of unification in the context of term indexing, we made large-scale 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.

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Section: Benchmarking Methodologymentioning

confidence: 99%

“…According to [12], indexing data structures are well-known to be crucial for the efficiency of the current state-of-the-art theorem 2 provers. Indexes in theorem provers frequently store 10 5 -10 6 complex terms and are highly dynamic since terms are frequently inserted in and deleted from indexes.…”

Section: Introductionmentioning

confidence: 99%

Comparing Unification Algorithms in First-Order Theorem Proving

Hoder

Воронков

2009

KI 2009: Advances in Artificial Intelligence

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“…Our implementation of an equational prover is based on the inference rules for unfailing completion as presented in Hsiang and Rusinowitch (1987) and Bachmair et al (1989). We use three sets of term pairs to represent the current state of a completion process: A set E of processed, but unorientable equations, a set R of rules (processed and oriented equations), and a set CP of unprocessed equations.…”

Section: Distributed Equational Reasoning-the Discount Systemmentioning

confidence: 99%

“…Our implementation of a deduction system using TEAMWORK is the DISCOUNT system (DIStributed COMpletion UsiNg Teamwork ) for equational reasoning [Avenhaus et al (1995)]. In order to discuss specific problems we have to introduce some concepts of equational reasoning.…”

Section: Distributed Equational Reasoning-the Discount Systemmentioning

confidence: 99%

Recording and Analysing Knowledge-Based Distributed Deduction Processes

Denzinger

Schulz²

1996

Journal of Symbolic Computation

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Distributed models for deduction allow for more powerful proof systems, but also lead to new problems. In particular, the analysis of the deduction process becomes harder, as a number of largely independent agents may contribute to the proof. In a system including cooperating agents, timing considerations can lead to further problems.In this paper we first introduce the TEAMWORK method and the DISCOUNT system for distributed equational reasoning. We point out the difficulties in obtaining a detailed representation of the proofs generated by a distributed system with completely distributed memory and present our solution for the TEAMWORK approach. Using this solution we are able to explain some of the speed-ups DISCOUNT was able to obtain in distributed mode. We also show how the representation of an equational proof as a listing of inferences can be transformed into a proof easily readable by human beings. Finally, pruned proof protocols (containing only facts contributing to the proof) also enable us to develop new, adaptive strategies for the proof search.

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“…There has been work in the past on combining different solvers/calculi or different instances of the same solver/calculus in a run by exchanging results, e.g., [2,8]. However, none of these approaches matured or survived.…”

Section: Sm-portfolio Solversmentioning

confidence: 99%

Do Portfolio Solvers Harm?

Weidenbach

EPiC Series in Computing

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DISCOUNT: A system for distributed equational deduction

Cited by 32 publications

References 4 publications

Comparing Unification Algorithms in First-Order Theorem Proving

Comparing Unification Algorithms in First-Order Theorem Proving

Recording and Analysing Knowledge-Based Distributed Deduction Processes

Do Portfolio Solvers Harm?

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