Ryuzo Hasegawa

Embedding Negation as Failure into a Model Generation Theorem Prover

Here, for the first time, we give an implementation which computes answer sets of every class of (function-free) logic programs and deductive databases containing both negation as failure and classical negation. The proposal is based on bottom-up, incremental, backtrack-free computation of the minimal models of positive disjunctive programs, together with integrity constraints over beliefs and disbeliefs. Our translation method not only provides a simple fixpoint characterization of answer sets, but also is very helpful to understand under what conditions each model is “stable” or “unstable”. The procedure has been implemented on top of the model generation theorem prover MGTP on a parallel inference machine, and has been applied to a legal reasoning system.

Implementation and evaluation of a list-processing-oriented data flow machine

The architecture of a data flow machine, called DFM, is developed for parallel list processing. The DFM can maximally exploit parallelism inherent in list processing, due to its ultra-multi-processing mechanism, packet communication-based parallel and pipeline execution mechanism, and lenient cons mechanism. A practical DFM implementation is described. A DFM prototype machine is implemented and DFM performance is evaluated in a simulation on the register transfer level using several benchmark programs. The DFM single processor system is shown to be about five times faster than conventional machines which use the same device technology, while a multi-processor DFM system is shown to achieve a linear speed-up ratio of 0.6 ~ 0.9.

Dataflow computing and eager and lazy evaluations

Eager and lazy evaluations in a dataflow model are proposed, Such evaluation enables nonstrict evaluation, structure data manipulation and nondeterminate computation. Several dataflow computation models are discussed from the viewpoint of their by-value and by-reference mechanisms, i. e., their token to data correspondence. It is shown that effective implementation is achieved by unifying both mechanisms. This implies the effective implementation of the lenient cons and lazy cons concept in list manipulation. Nonstrict list manipulation is shown to be useful for stream-oriented processing, and for nondeterminate computation combined with the nonstrict primitive operator, Arbiter. Several sample programs are included to show that concurrent processes and object-oriented programs can be intuitively described in functional language.

A list-processing-oriented data flow machine architecture

This paper analyzes some issues concerning list processing under a data flow control environment from the viewpoint of parallelism and also presents a new type of list-processing-oriented data flow machine, based on an association memory and logic-in-memory. The mechanism of partial execution in each function is shown by example to be effective in exploiting the parallelism in list processing. The lenient cons mechanism is shown to exploit maximally parallelism among activated functions.

Non-Horn Magic Sets to Incorporate Top-down Inference into Bottom-up Theorem Proving

We present a new method, called non-Horn magic sets (NHM), to enhance forward reasoning provers by combining top-down and bottom-up computations. This method is a natural extension of Horn magic sets and is applicable to range-restricted non-Horn clauses. We show two types of transformations to get non-Horn magic sets from the given clause sets: breadth-first NHM and depth-first NHM. The first transformation evaluates the antecedent atoms of an original clause in parallel. The second one evaluates them sequentially while propagating the bindings in an antecedent atom to the next by using continuation predicates. These transformations are shown to be sound and complete. The NHM method has been implemented on a UNIX workstation. We evaluated effects of NHM by proving some typical problems taken from the TPTP problem library.

MGTP: A Parallel Theorem Prover Based on Lazy Model Generation

We have implemented a model-generation based parallel theorem prover in KL1 on a parallel inference machine, PIM. We have developed several techniques to improve the efficiency of forward reasoning theorem provers based on lazy model generation. The tasks of the model-generation based prover are the generation and testing of atoms to be the elements of a model for the given theorem. The problem with this method is the explosion in the number of generated atoms and in the computational cost in time and space, incurred by the generation processes. Lazy model generation is a new method that avoids the generation of unnecessary atoms that are irrelevant to obtaining proofs, and to provide flexible control for the efficient use of resources in a parallel environment. With this method we have achieved a more than one-hundred-fold speedup on a PIM consisting of 128 PEs.

Modulo Based CNF Encoding of Cardinality Constraints and Its Application to MaxSAT Solvers

Totalizer (TO) by Bailleux et al. and Half Sorting Network (HS) by Asin et al. are typical CNF encoding methods of cardinality constraint. The former is based on unary adder, while the latter is based on odd-even merge. Although TO is inferior to HS in terms of the number of clauses, TO is superior to HS in terms of the number of variables. We propose a new method called Modulo Totalizer (MTO) to overcome the disadvantage of TO. As an application, we have developed a partial MaxSAT solver with MTO. Preliminary experimental results show that our MTO based MaxSAT solver is comparable to or surpass the conventional TO based maxsat solvers.

Efficient Minimal Model Generation Using Branching Lemmas

An efficient method for minimal model generation is presented. The method employs branching assumptions and lemmas so as to prune branches that lead to nonminimal models, and to reduce minimality tests on obtained models. This method is applicable to other approaches such as Bry’s complement splitting and constrained search or Niemela’s groundedness test, and greatly improves their efficiency. We implemented MM-MGTP based on the method. Experimental results with MM-MGTP show a remarkable speedup compared to MM-SATCHMO.

MGTP: A Model Generation Theorem Prover - Its Advanced Features and Applications

This paper outlines a parallel model-generation based theorem-proving system MGTP that we have been developing, focusing on the recent developments including novel techniques for efficient proof-search and successful applications.

On the Relationship Between Non-Horn Magic Sets and Relevancy Testing

Model-generation based theorem provers such as SATCHMO and MGTP suffer from a combinatorial explosion of the search space caused by clauses irrelevant to the goal (negative clause) to be solved. To avoid this, two typical methods have been proposed. One is relevancy testing implemented in SATCHMORE by Loveland et al., and the other is non-Horn magic sets that are the extension of Horn magic sets and used for MGTP. In this paper, we define the concept of weak relevancy testing, which somewhat relaxes the relevancy testing constraint. Then, we analyze the relationship between non-Horn magic sets and weak relevancy testing in detail, and prove that the total number of interpretations generated by MGTP employing non-Horn magic sets is always the same as that by SATCHMORE using weak relevancy testing. Thus, we find that non-Horn magic sets and weak relevancy testing, although they are completely different approaches, have the same power in pruning redundant branches of a proof tree.