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Following an “unwritten tradition” this paper offers a review of another decade of achievements in the area of Spectral Techniques. Topics like transforms of matrix-valued functions, transforms based on non-Abelian groups, latest advancements related to Linear Independent transforms, a space-efficient algorithm to calculate spectral transforms, will be discussed. A special mention will be given to...
The task of modeling and reasoning about real-world problems often involves analyzing overconstrained representations, where not all constraints of a problem can be simultaneously satisfied. The need to analyze over-constrained (or unsatisfiable) problems occurs in many settings, including data and knowledge bases, artificial intelligence, applied formal methods, operations research and description...
Multiway Decision Graphs (MDGs) subsume Binary Decision Diagrams(BDDs) and extend them by a first-order formulae suitable for model checking of data path circuits. In this paper, we propose a reduction technique to improve MDGs model checking. We use a reduction platform based on combining MDGs together with the rewriting engine in the HOL theorem prover. The idea is to prune the transition relation...
We investigate the automorphism group of finite Gödel algebras, the algebraic counterpart of Godel infinite-valued propositional logic with a finite number of variables. In logical terms, we look at the structure of substitution of terms that preserve logical equivalence in this logic. We obtain a characterisation of the arising automorphism groups in terms of semidirect and direct products of symmetric...
The theory of Schauder hats is a beautiful and powerful tool for investigating, under several respects, the algebraic semantics of Łukasiewicz infinite-valued logic [CDM99],[MMM07], [Mun94], [P95]. As a notably application of the theory, the elements of the free n-generated MV-algebra, that constitutes the algebraic semantics of the n-variate fragment ofŁukasiewicz logic, are...
In this paper, a theory of multiple-valued threshold functions over the field of complex numbers is further developed. k-valued threshold functions over the field of complex numbers can be learned using a single multi-valued neuron (MVN). We propose a new approach for the projection of a k-valued function, which is not a threshold one, to m-valued logic (m≫k), where this function becomes a partially...
This paper presents a new algorithm MP(multiple pass) to synthesize large reversible binary circuits without ancilla bits. The MMD algorithm requires to store a truth table (or a Reed-Muller -RM transform) as a 2^n vector for a reversible function of n variables. This representation prohibits synthesis of large functions. However, in MP we do not store such an exponentially growing data structure...
We analyze the existing encodings from MaxCSP into Partial MaxSAT, and report on a number of new insights that we have gained from our analysis, which can be summarized as follows: (i) the at-most-one (AMO) condition can be omitted in direct encodings from MaxCSP into Partial MaxSAT, and auxiliary variables are not needed; (ii) the sequential encoding of the cardinality constraint is, in fact, a reformulation...
Non-deterministic multi-valued matrices (Nmatrices) are a new, fruitful and quickly expanding field of research first introduced a few years ago. Since then it has been rapidly developing towards a foundational logical theory and has found numerous applications. The novelty of Nmatrices is in extending the usual many-valued algebraic semantics of logical systems by importing the idea of non-deterministic...
Extending the work of Belnap [3], we continue our research on ESP structures, consisting of information sources and a processor which collects information from the sources, and develops it further using certain coherent rules. We examine the case of reasonable sources which provide coherent information, characterize the logic of a single reasonable source, and prove that the logics generated by ESP...
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