A thorough algebraic method is described for the determination of the complete set of irre-dundant normal and conjunctive forms of a Boolean function. The method is mechanical and therefore highly programmable on a computer.

In this paper we present a new upper bound for randomly chosen 3-CNF formulas. In particular we show that any random formula over n variables, with a clauses-to-variables ratio of at least 4.4898 is, as n grows large, asymptotically almost surely unsatisfiable. The previous best such bound, due to Dubois in 1999, was 4.506. The first such bound, independently discovered by many groups of resear...

A Pseudo-Boolean constraint is a linear constraint over Boolean variables. This kind of constraints has been widely used in expressing NP-complete problems. This paper introduces a new algorithm for translating Pseudo-Boolean constraints into CNF clauses. The CNF produced by the proposed encoding has small size, and we also characterize the constraints for which one can expect the SAT solvers t...

Article history: Received 19 December 2008 Received in revised form 11 June 2009 Accepted 13 June 2009 Available online 17 June 2009

The paper discusses the modeling of “if possible" in requirements of the form “A and if possible B". We distinguish between two types of understanding: either i) A and B are requirements of the same nature and are viewed as constraints with different levels of priority, or ii) they are of different nature (only A induces constraint(s) and B is only used for breaking ties among items that are eq...

We survey recent results on difference sets, p-ranks and Smith normal forms of certain set-inclusion matrices and subspace-inclusion matrices.

Dempster’s rule plays a central role in the theory of belief functions. However, it assumes the combined bodies of evidence to be distinct, an assumption which is not always verified in practice. In this paper, a new operator, the cautious rule of combination, is introduced. This operator is commutative, associative and idempotent. This latter property makes it suitable to combine belief functi...

Kuroda (1979) argues that Japanese ni yotte passives are derived by movement of an underlying internal argument to subject position. The socalled syntactic passive pattern in Korean, derived with the bound verb -ci ‘become’, also gives strong evidence for a movement derivation (see Park 2001). Facts like those in (1-3) below support the movement analysis: (1-2) show that subject position is not...

Commonly used gralm~mrs which describe i~turai lan~uages /ex. ATN, Metamorphosis Grammars/ can be hardly applied in describing higly inflectional languages. So I propose a grammar called the grammar with natural context which takes into consideration properties of higly inflectional languages /ex. Polish / as well as structural languages /ex. English/. I introduce its normal form.