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A quantum storage device differs radically from a conventional physical storage device. Its state can be set to any value in a certain (infinite) state space, but in general every possible read operation yields only partial information about the stored state. The purpose of this paper is to initiate the study of a combinatorial abstraction, called abstract storage device (ASD), which models deterministic storage devices with the property that only partial information about the state can be read, but that there is a degree of freedom as to which partial information should be retrieved. This concept leads to a number of interesting problems which we address, like the reduction of one device to another device, the equivalence of devices, direct products of devices, as well as the factorization of a device into primitive devices. We prove that every ASD has an equivalent ASD with minimal number of states and of possible read operations. Also, we prove that the reducibility problem for ASDs is NP-complete, that the equivalence problem is at least as hard as the graph isomorphism problem, and that the factorization into binary-output devices (if it exists) is unique.
This is an extended abstract presenting new results on the topological complexity of omega-powers (which are included in a paper Classical and effective descriptive complexities of omega-powers available from arXiv:0708.4176) and reflecting also some
This paper has been withdrawn because Theorem 21 and Corollary 22 are in error; The modeling idea is OK, but it needs 9-dimensional variables instead of the 8-dimensional variables defined in notations 6.9. Examples of the correct model (with 9-ind
This paper deals with the theory and application of 2-Dimensional, nine-neighborhood, null- boundary, uniform as well as hybrid Cellular Automata (2D CA) linear rules in image processing. These rules are classified into nine groups depending upon the
In this paper, we present a new, graph-based modeling approach and a polynomial-sized linear programming (LP) formulation of the Boolean satisfiability problem (SAT). The approach is illustrated with a numerical example.
For a set A of n applicants and a set I of m items, we consider a problem of computing a matching of applicants to items, i.e., a function M mapping A to I; here we assume that each applicant $x in A$ provides a preference list on items in I. We say