Improvements of the Construction of Exact Minimal Covers of Boolean Functions
نویسندگان
چکیده
The calculation of an exact minimal cover of a Boolean function is an NP -complete problem. In this paper we introduce the definition of this problem and its basic solution. By using a slightly modified algorithm, we get a speed-up factor of more than 10. The main contributions of this paper are the description of an alternative approach mentioned in [15], and a remarkable improvement of this algorithm. In both cases operations of the XBOOLE library are used. Using the newly suggested algorithm, the time required for the calculation could be reduced by a factor of more than 8 ∗ 10 in comparison with the previous algorithm.
منابع مشابه
New Results for Sets of Boolean Functions
Traditionally Sum-Of-Products (SOPs) have been studied as expressions of Boolean functions. It has been shown by Sasao in [7] that Exclusive-or-Sum-Of-Products (ESOPs) are more compact representations of Boolean functions than SOPs. The problem to identify an exact minimal ESOP of a Boolean function is despite of some partial results still unsolved. Our new results rely on recently detected pro...
متن کاملON THE FUZZY SET THEORY AND AGGREGATION FUNCTIONS: HISTORY AND SOME RECENT ADVANCES
Several fuzzy connectives, including those proposed by Lotfi Zadeh, can be seen as linear extensions of the Boolean connectives from the scale ${0,1}$ into the scale $[0,1]$. We discuss these extensions, in particular, we focus on the dualities arising from the Boolean dualities. These dualities allow to transfer the results from some particular class of extended Boolean functions, e.g., from c...
متن کاملDetermination of Suitable Areas for underground Dam Construction Using Boolean and Fuzzy Logics in Central Areas of Ardebil Province
In the arid and semi-arid area's rainfall have considerable changes in terms of time and amount that make the water resource management an important issue. In this research, using both Boolean and Fuzzy logic were zoned potentiality suitable areas for construction of underground dams. The study area is located in the central region of Ardabil province with 7461 km2 area and semi-arid climate. F...
متن کاملConstructing Parsimonious Hybridization Networks from Multiple Phylogenetic Trees Using a SAT-Solver
We present an exact algorithm for constructing minimal hybridization networks from multiple trees which is based on reducing the problem to the Boolean satisfiability problem. The main idea of our algorithm is to iterate over possible hybridization numbers and to construct a Boolean formula for each of them that is satisfiable iff there exists a network with such hybridization number. The propo...
متن کاملExact Transversal Hypergraphs and Application to Boolean µ-Functions
Call an hypergraph, that is a family of subsets (edges) from a finite vertex set, an exact transversal hypergraph iff each of its minimal transversals, i.e., minimal vertex subsets that intersect each edge, meets each edge in a singleton. We show that such hypergraphs are recognizable in polynomial time and that their minimal transversals as well as their maximal independent sets can be generat...
متن کامل