ALGORITHM COMPARING BINARY STRING PROBABILITIES IN COMPLEX STOCHASTIC BOOLEAN SYSTEMS USING INTRINSIC ORDER GRAPH

Luis González ()
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Luis González: Department of Mathematics, University of Las Palmas de Gran Canaria, Campus Universitario de Tafira, 35017 Las Palmas de Gran Canaria, Spain

Advances in Complex Systems (ACS), 2007, vol. 10, issue supp0, 111-143

Abstract: This paper deals with a special kind of complex systems which depend on an arbitrary (and usually large) numbernof random Boolean variables. The so-called complex stochastic Boolean systems often appear in many different scientific, technical or social areas. Clearly, there are2nbinary states associated to such a complex system. Each one of them is given by a binary stringu = (u1,…,un) ∈ {0, 1}nofnbits, which has a certain occurrence probabilityPr{u}. The behavior of a complex stochastic Boolean system is determined by the current values of its2nbinaryn-tuple probabilitiesPr{u}and by the ordering between pairs of them. Hence, the intrinsic order graph provides a useful representation of these systems by displaying (scaling) the2nbinaryn-tuples which are ordered in decreasing probability of occurrence. The intrinsic order reduces the complexity of the problem from exponential (2nbinaryn-tuples) to linear (nBoolean variables). For any fixed binaryn-tupleu, this paper presents a new, simple algorithm enabling rapid, elegant determination of all the binaryn-tuplesvwith occurrence probabilities less than or equal to (greater than or equal to)Pr{u}. This algorithm is closely related to the lexicographic (truth-table) order in{0, 1}n, and this is illustrated through the connections (paths) in the intrinsic order graph.

Keywords: Complex stochastic Boolean system; binary string probabilities; lexicographic order; intrinsic order; algorithm (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1142/S0219525907001136

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