﻿ Complexity of Boolean functions in intelligent systems …

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## This paper studies the implementation of Boolean functions ..

Complexity of Boolean functions in intelligent systems for synthesis of digital integrated circuits

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# Gate-Level Synthesis of Boolean Functions Using Binary ..

The sequence of operations performed by hardware or software. It is the computer's "intelligence." Hardware logic is contained in the electronic circuits and follows the rules of Boolean logic. Software logic (program logic) is contained in the placement of instructions written by the programmer. Software logic is called "business logic" when it refers to the transactions of the business rather than underlying infrastructure such as the operating system, database management system (DBMS) or network.Logic Is Not LogicalThe term "logic" is not the same as "logical." Logic refers to algorithms and operational sequences; whereas, "logical" refers to a higher-level view of hardware, software or data that is not tied to physical structures (see ). See also .

Stochastic computing (SC) uses standard logic to process pseudo-random bit-streams denoting probabilities. It implements arithmetic operations by extremely simple and low-power hardware. Despite major new applications, SC's theory and design requirements are poorly understood. We observe that the Boolean functions used in SC take the form f(X) = f(XV;XC), where XV and XC are inputs with variable and constant probabilities, respectively. Different functions can be equivalent in the sense of implying the same stochastic behavior. We define stochastic equivalence classes (SECs), and investigate their properties and applications. Suitably interpreted, SECs describe all realizable arithmetic functions of interest. While conventional synthesis focuses on finding the best circuit to implement a known function, stochastic circuit optimization first requires finding the best function. We present an SEC-based approach to this problem, which demonstrates the computational richness of SC and leads to significant cost reductions compared to prior designs.

## Logic Friday - Free software for boolean logic analysis

...n linear) fan-in values. They have applications to hardware implementations of neural networks. The first approach is based on implementing a certain sub-class of Boolean functions, IF n, m functions =-=[34]-=-. We will show that this class of functions can be implemented in VLSI-optimal (i.e., minimising AT 2 ) neural networks of small constant fan-ins. The second approach is based on implementing Boolean ...

This paper studies the implementation of Boolean functions by lattices of four-terminal switches. Each switch is controlled by a Boolean literal. If the literal takes the value 1, the corresponding switch is connected to its four neighbors; else it is not connected. A Boolean function is implemented in terms of connectivity across the lattice: it evaluates to 1 iff there exists a connected path between two opposing edges of the lattice. The paper addresses the following synthesis problem: how should one assign literals to switches in a lattice in order to implement a given target Boolean function? The goal is to minimize the lattice size, measured in terms of the number of switches. An efficient algorithm for this task is presented-one that does not exhaustively enumerate paths but rather exploits the concept of Boolean function duality. The algorithm produces lattices with a size that grows linearly with the number of products of the target Boolean function in ISOP form. It runs in time that grows polynomially. Synthesis trials are performed on standard benchmark circuits. The synthesis results are compared to a lower-bound calculation on the lattice size.

## Logic dictionary definition | logic defined

The representation of an arbitrary Boolean function over different bases in classes of formulas and circuits of functional elements (with and without branching) is considered. It is accompanied by derivation of the corresponding (for different bases) estimates of the following complexity indices such as the number of letters and formula length, the number of subformulas and superposition formula depth, and the number of functional elements in the circuit and its depth. The obtained knowledge should be applied to intelligent systems of integrated circuit synthesis.

Number systems, Boolean algebra, Boolean functions, and function minimization. Analysis and design of combinational and sequential logic circuits. Hardware Description Language (HDL) concepts and applications digital design and synthesis in Programmable Logic Devices (PLDs). Not open to students with credit in CPE/EE 129. Course may be offered in classroom-based or online format. 3 lectures, 1 laboratory. Crosslisted as CPE/.

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Boolean algebra - Wikipedia

## Evolutionary Synthesis of Logic Circuits Using …

AB - Stochastic computing (SC) uses standard logic to process pseudo-random bit-streams denoting probabilities. It implements arithmetic operations by extremely simple and low-power hardware. Despite major new applications, SC's theory and design requirements are poorly understood. We observe that the Boolean functions used in SC take the form f(X) = f(XV;XC), where XV and XC are inputs with variable and constant probabilities, respectively. Different functions can be equivalent in the sense of implying the same stochastic behavior. We define stochastic equivalence classes (SECs), and investigate their properties and applications. Suitably interpreted, SECs describe all realizable arithmetic functions of interest. While conventional synthesis focuses on finding the best circuit to implement a known function, stochastic circuit optimization first requires finding the best function. We present an SEC-based approach to this problem, which demonstrates the computational richness of SC and leads to significant cost reductions compared to prior designs.

## Evolutionary Synthesis of Logic Circuits Using Information Theory

N2 - Stochastic computing (SC) uses standard logic to process pseudo-random bit-streams denoting probabilities. It implements arithmetic operations by extremely simple and low-power hardware. Despite major new applications, SC's theory and design requirements are poorly understood. We observe that the Boolean functions used in SC take the form f(X) = f(XV;XC), where XV and XC are inputs with variable and constant probabilities, respectively. Different functions can be equivalent in the sense of implying the same stochastic behavior. We define stochastic equivalence classes (SECs), and investigate their properties and applications. Suitably interpreted, SECs describe all realizable arithmetic functions of interest. While conventional synthesis focuses on finding the best circuit to implement a known function, stochastic circuit optimization first requires finding the best function. We present an SEC-based approach to this problem, which demonstrates the computational richness of SC and leads to significant cost reductions compared to prior designs.

## Logic synthesis for switching lattices — …

AB - This paper studies the implementation of Boolean functions by lattices of four-terminal switches. Each switch is controlled by a Boolean literal. If the literal takes the value 1, the corresponding switch is connected to its four neighbors; else it is not connected. A Boolean function is implemented in terms of connectivity across the lattice: it evaluates to 1 iff there exists a connected path between two opposing edges of the lattice. The paper addresses the following synthesis problem: how should one assign literals to switches in a lattice in order to implement a given target Boolean function? The goal is to minimize the lattice size, measured in terms of the number of switches. An efficient algorithm for this task is presented-one that does not exhaustively enumerate paths but rather exploits the concept of Boolean function duality. The algorithm produces lattices with a size that grows linearly with the number of products of the target Boolean function in ISOP form. It runs in time that grows polynomially. Synthesis trials are performed on standard benchmark circuits. The synthesis results are compared to a lower-bound calculation on the lattice size.

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