Genetic Strategy Selection for Parallel Theorem Proving

Automated theorem provers use search strategies for accomplishing their proof tasks. Unfortunately, there is no unique strategy which is uniformly successful and uniformly fast on all problems. The combination of more than one strategy in parallel leads to a decreasing response time compared with sequential approaches and to an increasing number of solutions found. Limited availability of resources as time or processors necessitates the efficient use of these resources by partitioning the resources adequately among the involved strategies. We describe the paradigm of strategy parallelism for general search problems, and sketch some problems which have to be solved when constructing and configuring a strategy parallel prover. Then we present a solution for this prover configuration problem which works quickly, with high precision, and fully automatically. We finish giving some experimental data for our implementation of this concept, that has been proven to be one of the fastest availab..

Unit Propagation in a Tableau Framework ⋆

Abstract. Unit propagation is one of the most important techniques of efficient SAT solvers. Unfortunately, this technique is not directly applicable to first-order clausal tableaux. We show a way of integrating a variant of unit propagation into the disconnection calculus and present some results obtained with an implementation of unit propagation in the DCTP theorem prover that show the usefulness of our new method.

Proof Output and Transformation for Disconnection Tableaux ⋆

Abstract. For applications of first-order automated theorem provers in a wider verification context it is essential to provide a means of presenting and checking automatically found proofs. In this paper we present a new method of transforming disconnection tableau proofs found by the prover system DCTP into a series of resolution inferences representing a resolution refutation of the proof problem.

Proof transformations from search-oriented into interaction-oriented tableau calculi

Abstract: Logic calculi, and Gentzen-type calculi in particular, can be categorised into two types: search-oriented and interaction-oriented calculi. Both these types have certain inherentcharacteristics stemming from the purpose for which they are designed. In this paper, we give a general characterisation of the two types and present two calculi that are typical representatives of their respective class. We introduce a method for transforming proofs in the search-oriented calculus into proofs in the interactionoriented calculus, and we demonstrate that the di culties arising with devising such a transformation do not pertain to the speci c calculi we have chosen as examples but are general. We also give examples for the application of our transformation procedure

P-SETHEO: Strategy Parallel Automated Theorem Proving

One of the key issues in Automated Theorem Proving is the search for optimal proof strategies. Since there is not one uniform strategy which works optimal on all proof tasks, one is faced with the difficult problem of selecting a good strategy for a given task. In this paper, we discuss a way of circumventing this strategy selection problem by using strategy parallelism. In this approach, a proof task is attempted in parallel by a set of uniform strategies while distributing the given amount of computing resources according to a certain schedule. We discuss important issues of strategy parallelism like search space partitioning, schedule computation, and scalability. In order to evaluate the potential of the method experimentally, we have implemented the strategy parallel theorem prover p-SETHEO, which is also described in the paper. The experimental results obtained with the system justify our approach. 1 Introduction Automated Theorem Proving (ATP) is the subfield of theoretical co..