scholarly journals A Domain-Transformation Approach to Synthesize Read-Polarity-Once Boolean Functions

2014 ◽  
Vol 9 (1) ◽  
pp. 60-69
Author(s):  
Vinicius Callegaro ◽  
Mayler G. A. Martins ◽  
Renato P. Ribas ◽  
André I. Reis
Keyword(s):  
Boolean Functions ◽  
Experimental Results ◽  
Boolean Expression ◽  
Transformation Approach ◽  
Domain Transformation

Efficient exact factoring algorithms are limited to read-once (RO) functions, where each variable appears exactly once at the final Boolean expression. However, these algorithms present two important constraints: (1) they do not consider incompletely specified Boolean functions (ISFs), and (2) they are not suitable for binate functions. To overcome the first drawback, an algorithm that finds RO expressions for ISF, whenever possible, is proposed. In respect to the second limitation, we propose a domain transformation that splits existing binate variables into two independent unate variables. Such a domain transformation leads to ISFs, which can be efficiently factored by applying the proposed algorithm. The combination of both contributions gives optimal results for a recently proposed broader class of Boolean functions called read-polarity-once (RPO) functions, where each polarity (positive and negative) of a variable appears at most once in the factored form. Experimental results carried out over ISCAS’85 benchmark circuits have shown that RPO functions are significantly more frequent than RO functions.

SAT-Based Generation of Optimum Circuits with Polymorphic Behavior Support

2019 ◽  
Vol 28 (supp01) ◽  
pp. 1940010
Author(s):  
Petr Fišer ◽  
Ivo Háleček ◽  
Jan Schmidt ◽  
Václav Šimek
Keyword(s):  
Boolean Functions ◽  
Equivalence Classes ◽  
Experimental Results ◽  
Behavior Support ◽  
Operating Environment ◽  
Polymorphic Behavior ◽  
Multi Level ◽  
Boolean Optimization ◽  
Hardware Structure

This paper presents a method for generating optimum multi-level implementations of Boolean functions based on Satisfiability (SAT) and Pseudo-Boolean Optimization (PBO) problems solving. The method is able to generate one or enumerate all optimum implementations, while the allowed target gate types and gates costs can be arbitrarily specified. Polymorphic circuits represent a newly emerging computation paradigm, where one hardware structure is capable of performing two or more different intended functions, depending on instantaneous conditions in the target operating environment. In this paper we propose the first method ever, generating provably size-optimal polymorphic circuits. Scalability and feasibility of the method are documented by providing experimental results for all NPN-equivalence classes of four-input functions implemented in AND–Inverter and AND–XOR–Inverter logics without polymorphic behavior support being used and for all pairs of NPN–equivalence classes of three-input functions for polymorphic circuits. Finally, several smaller benchmark circuits were synthesized optimally, both in standard and polymorphic logics.

scholarly journals Bi-Kronecker Functional Decision Diagrams: A Novel Canonical Representation of Boolean Functions

2019 ◽  
Vol 33 ◽  
pp. 2867-2875 ◽  
Author(s):  
Xuanxiang Huang ◽  
Kehang Fang ◽  
Liangda Fang ◽  
Qingliang Chen ◽  
Zhao-Rong Lai ◽  
...  
Keyword(s):  
Data Structure ◽  
Boolean Functions ◽  
Canonical Representation ◽  
Experimental Results ◽  
Compact Representation ◽  
Decision Diagrams ◽  
Canonical Forms

In this paper, we present a novel data structure for compact representation and effective manipulations of Boolean functions, called Bi-Kronecker Functional Decision Diagrams (BKFDDs). BKFDDs integrate the classical expansions (the Shannon and Davio expansions) and their bi-versions. Thus, BKFDDs are the generalizations of existing decision diagrams: BDDs, FDDs, KFDDs and BBDDs. Interestingly, under certain conditions, it is sufficient to consider the above expansions (the classical expansions and their bi-versions). By imposing reduction and ordering rules, BKFDDs are compact and canonical forms of Boolean functions. The experimental results demonstrate that BKFDDs outperform other existing decision diagrams in terms of sizes.

Application of Indexed Partition Calculus in Logic Synthesis of Boolean Functions for FPGAs

2011 ◽  
Vol 57 (2) ◽  
pp. 209-216 ◽  
Author(s):  
Mariusz Rawski
Keyword(s):  
Boolean Functions ◽  
Logic Synthesis ◽  
Experimental Results ◽  
Computation Complexity ◽  
Functional Decomposition ◽  
Partition Calculus ◽  
Input And Output ◽  
Decomposition Of Boolean Functions

Application of Indexed Partition Calculus in Logic Synthesis of Boolean Functions for FPGAsFunctional decomposition of Boolean functions specified by cubes proved to be very efficient. Most popular decom-position methods are based on blanket calculus. However computation complexity of blanket manipulations strongly depends on number of function's variables, which prevents them from being used for large functions of many input and output variables. In this paper a new concept of indexed partition is proposed and basic operations on indexed partitions are defined. Application of this concept to logic synthesis based on functional decomposition is also discussed. The experimental results show that algorithms based on new concept are able to deliver good quality solutions even for large functions and does it many times faster than the algorithms based on blanket calculus.

SEMANTIC SEARCH TECHNIQUES FOR LEARNING SMALLER BOOLEAN EXPRESSION TREES IN GENETIC PROGRAMMING

2014 ◽  
Vol 13 (03) ◽  
pp. 1450018
Author(s):  
NICHOLAS C. MILLER ◽  
PHILIP K. CHAN
Keyword(s):  
Genetic Programming ◽  
Semantic Search ◽  
Experimental Results ◽  
Boolean Expression ◽  
Mutation Operators ◽  
Recent Interest ◽  
Program Semantics ◽  
Large Program ◽  
Crossover And Mutation ◽  
Better Than

One sub-field of Genetic Programming (GP) which has gained recent interest is semantic GP, in which programs are evolved by manipulating program semantics instead of program syntax. This paper introduces a new semantic GP algorithm, called SGP+, which is an extension of an existing algorithm called SGP. New crossover and mutation operators are introduced which address two of the major limitations of SGP: large program trees and reduced accuracy on high-arity problems. Experimental results on "deceptive" Boolean problems show that programs created by the SGP+ are 3.8 times smaller while still maintaining accuracy as good as, or better than, SGP. Additionally, a statistically significant improvement in program accuracy is observed for several high-arity Boolean problems.

Logic Design Using Modules and Nonlinear Integer Programming

2020 ◽  
Vol 29 (10) ◽  
pp. 2050164
Author(s):  
C. Pavlatos ◽  
A. C. Dimopoulos ◽  
G. Papakonstantinou
Keyword(s):  
Integer Programming ◽  
Boolean Functions ◽  
Logic Gates ◽  
Logic Circuits ◽  
Experimental Results ◽  
Nonlinear Integer Programming ◽  
Uniform Structure ◽  
Logic Design ◽  
Nonlinear Approach

Using logic gates is the traditional way of designing logic circuits. However, in many cases, the use of modules is advantageous as the module is considered a uniform structure composed of multiple gates. In this paper, a nonlinear approach is proposed for designing logic circuits for use as modules multiplexers (MUXs) or Reed–Muller universal blocks (RMs). The experimental results show that the method gives better results compared to other methods available in the literature. The main advantages of the method are that it guarantees minimality and it can also handle Boolean functions for incompletely specified functions. The method is general enough and can be used for any kind of modules.

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