9 We study algorithms for � SAT and its generalized version � GENSAT, the problem of computing th... more 9 We study algorithms for � SAT and its generalized version � GENSAT, the problem of computing the number of satisfying assignments of a set of propositional clauses . For this purpose we consider the clauses given by their incidence graph, a signed 11 bipartite graph SI(), and its derived graphs I( ) and P( ). It is well
A Computational Framework for the Study of Partition Functions and Graph Polynomials
2012 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 2012
ABSTRACT Partition functions and graph polynomials have found many applications in combinatorics,... more ABSTRACT Partition functions and graph polynomials have found many applications in combinatorics, physics, biology and even the mathematics of finance. Studying their complexity poses some problems. To capture the complexity of their combinatorial nature, the Turing model of computation and Valiant's notion of counting complexity classes seem most natural. To capture the algebraic and numeric nature of partition functions as real or complex valued functions, the Blum-Shub-Smale (BSS) model of computation seems more natural. As a result many papers use a naive hybrid approach in discussing their complexity or restrict their considerations to sub-fields of C which can be coded in a way to allow dealing with Turing computability. In this paper we propose a unified natural framework for the study of computability and complexity of partition functions and graph polynomials and show how classical results can be cast in this framework.
References Cou93] B. Courcelle. The monadic second{order logic of graphs IX: Machines and their b... more References Cou93] B. Courcelle. The monadic second{order logic of graphs IX: Machines and their behaviours. Preprint, 1993. Cou94] B. Courcelle. Monadic second order graph transductions: A survey. Theoretical Computer Science, 126:53{75, 1994. CW95] B. Courcelle and I. Walukiewicz. Monadic second order logic, graphs and unfoldings of transition systems. Paper in preparation, 1995. Dah82] E. Dahlhaus. Combinatorial and Logical Properties of Reductions to some Complete Problems in NP and NL. PhD thesis,
Translation schemes and the fundamental problem of database design
Lecture Notes in Computer Science, 1996
We introduce a new point of view into database schemes by applying systematically an old logical ... more We introduce a new point of view into database schemes by applying systematically an old logical technique: translation schemes, and their induced formula and structure transformations. This allows us to re-examine the notion of dependency preserving decomposition and its generalization refinement.
2013 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 2013
ABSTRACT In this paper, we try to build a bridge between pure theoretical approach to computation... more ABSTRACT In this paper, we try to build a bridge between pure theoretical approach to computations on decomposable graphs and heuristics, used in practice for treatment of particular cases of them. In theory, Feferman and Vaught in 1959 proposed a method to reduce solution of First Order definable problems on Disjoint Union of structures to solutions of derived problems on the components with some post-processing of the obtained results. In practice, the literature is very reach in examples of particular methods to deal with different variations of graphs, built from components. From the theoretical point of view we adapt and generalize the Feferman-Vaught method. We define a new kind of decomposable graphs: sum-like graphs and propose a new systematic approach, which allows us to reduce the solution of Monadic Second Order definable problems on such graphs to the solution of effectively derivable Monadic Second Order definable problems on the components. From the practical point of view, we consider in great details one application of our approach in the field of parallel computations on distributed data.
ABSTRACT Boyce-Codd-Heath introduced criteria for good database design, which can be formulated i... more ABSTRACT Boyce-Codd-Heath introduced criteria for good database design, which can be formulated in terms of FD's only. Classical design decomposes relations iteratively using projections. BCNF can not be always achieved using projections alone. 3NF was introduced as a compromise. In this paper we summarize all the known characterizations of BCNF and formulate a new one. In [MR96], attribute splitting was suggested as a heuristics to achieve BCNF in case projections do not do the job. Here we show how attribute splitting can be used to restructure a database scheme iteratively such that the result will be in BCNF, is information preserving and preserves the functional dependencies.
ABSTRACT The dichromatic polynomial Z(G;q,v)Z(G;q,v) can be characterized as the most general C-i... more ABSTRACT The dichromatic polynomial Z(G;q,v)Z(G;q,v) can be characterized as the most general C-invariant, i.e., a graph polynomial satisfying a linear recurrence with respect to edge deletion and edge contraction. Similarly, the universal edge elimination polynomial ξ(G;x,y,z)ξ(G;x,y,z) introduced in [Ilya Averbouch, Benny Godlin, and Johann A. Makowsky. An extension of the bivariate chromatic polynomial. Eur. J. Comb, 31(1):1–17, 2010] can be characterized as the most general EE-invariant, i.e., a graph polynomial satisfying a linear recurrence with respect to edge deletion, edge contraction and edge extraction. In this paper we examine substitution instances of ξ(G;x,y,z)ξ(G;x,y,z) and show that among these the dichromatic polynomial Z(G;q,v)Z(G;q,v) plays a distinctive rôle.
Roots of graph polynomials such as the characteristic polynomial, the chromatic polynomial, the m... more Roots of graph polynomials such as the characteristic polynomial, the chromatic polynomial, the matching polynomial, and many others are widely studied. In this paper we examine to what extent the location of these roots reflects the graph theoretic properties of the underlying graph.
Dependency preserving refinements and the fundamental problem of database design
Data & Knowledge Engineering, 1998
... independence and avoid update anomalies; attaining of normal forms using dependencypreserving... more ... independence and avoid update anomalies; attaining of normal forms using dependencypreserving decompositions and ... the last section we draw our conclusions and sketch further research in progress. The use of translation schemes can be extended to a full fledged design ...
Counting truth assignments of formulas of bounded tree-width
... coloring. Given a graph G, nding its tree-width is NP-complete, cf. ACP87], but for xed k, ch... more ... coloring. Given a graph G, nding its tree-width is NP-complete, cf. ACP87], but for xed k, checking whether G has tree width at most k (and if yes, nding a witnessing tree decomposition), can be done in polynomial time, cf. Bod97]. ...
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Papers by Elena Ravve