Abstract: MINI is a heuristic logic minimization technique for many-variable problems. It accepts as input a Boolean logic specification expressed as an input-output table, thus avoiding a long list of minterms. It seeks a minimal implicant solution, without generating all prime implicants, which can be converted to prime implicants if desired. New and effective subprocesses, such as expanding, reshaping, and removing redundancy from cubes, are iterated until there is no further reduction in the solution. The process is general in that it can minimize both conventional logic and logic functions of multi-valued variables.

In this paper we describe an interior point mathematical programming approach to inductive inference. We list several versions of this problem and study in detail the formulation based on hidden Boolean logic. We consider the problem of identifying a hidden Boolean function F : f0; 1g n ! f0; 1g using outputs obtained by applying a limited number of random inputs to the hidden function. Given this input-output sample, we give a method to synthesize a Boolean function that describes the sample. We pose the Boolean Function Synthesis Problem as a particular type of Satisfiability Problem. The Satisfiability Problem is translated into an integer programming feasibility problem, that is solved with an interior point algorithm for integer programming. A similar integer programming implementation has been used in a previous study to solve randomly generated instances of the Satisfiability Problem. In this paper we introduce a new variant of this algorithm, where the Riemannian metric used...

Abstract. CirCUs is a satisfiability solver that works on a combination of an And-Inverter-Graph (AIG), Conjunctive Normal Form (CNF) clauses, and Binary Decision Diagrams (BDDs). We show how BDDs are used by CirCUs to help in the solution of SAT instances given in CNF. Specifically, the clauses are sorted by solving a hypergraph linear arrangement problem. Then they are clustered by an algorithm that strives to avoid explosion in the resulting BDD sizes. If clustering results in a single diagram, the SAT instance is solved directly. Otherwise, search for a satisfying assignment is conducted on the original clauses, enhanced with information extracted from the BDDs. We also describe a new decision variable selection heuristic that is based on recognizing that the variables involved in a conflict clause are often best treated as a related group. We present experimental results that demonstrate Cir-CUs’s efficiency especially for medium-size SAT instances that are hard to solve by traditional solvers based on DPLL. 1

A set of products is a prime cover of a Boolean function f if it is made of prime implicants of f , and if the sum of its products covers f . Finding a prime cover, an irredundant prime cover, or a minimal prime cover of a function f is a problem that arises in several fields of computer science, for instance in logic synthesis, automated reasoning, realiability analysis, and some optimization problems. This paper shows how the three prime cover computation problems mentioned above can be efficiently solved using implicit manipulations of sets of products. 1 Introduction Computing a prime cover, an irredundant prime cover, or a minimal prime cover of a Boolean function has several applications in computer science. In logic synthesis, an irredundant prime cover, or better, a minimal prime cover, provides the user with an efficient 2-level logic implementation of a single or multi output Boolean function [2, 24, 14]. In reliability analysis, prime covers are a way for either exhaustive...

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In an irredundant sum-of-products expression (ISOP), each product is a prime implicant (PI) and no product can be deleted without changing the function. Among the ISOPs for some function f, a worst ISOP (WSOP) is an ISOP with the largest number of PIs and a minimum ISOP (MSOP) is one with the smallest number. We show a class of functions for which the Minato-Morreale ISOP algorithm produces WSOPs. Since the ratio of the size of the WSOP to the size of the MSOP is arbitrarily large when n, the number of variables, is unbounded, the Minato-Morreale algorithm can produce results that are very far from minimum. We present a class of multiple-output functions whose WSOP size is also much larger than its MSOP size. For a set of benchmark functions, we show the distribution of ISOPs to the number of PIs. Among this set are functions where the MSOPs have almost as many PIs as do the WSOPs. These functions are known to be easy to minimize. Also, there are benchmark functions where the fraction of ISOPs that are MSOPs is small and MSOPs have many fewer PIs than the WSOPs. Such functions are known to be hard to minimize. For one class of functions, we show that the fraction of ISOPs that are MSOPs approaches 0 as n approaches infinity, suggesting that such functions are hard to minimize.

Reducing delay of a digital circuit is an important topic in logic synthesis for standard cells and LUT-based FPGAs. This paper presents a simple, fast, and very efficient synthesis algorithm to improve the delay after technology mapping. The algorithm scales to large designs and is implemented in a publicly-available technology mapper. The code is available online. Experimental results on industrial designs show that the method can improve delay by 30 % with the increase in area 2.4%, or by 41 % with the increase in area by 3.9%, on top of a high-effort synthesis and mapping flow. 1.

A transformation of multi-valued input binary-output functions, called co-singleton transform (CST), was introduced in [11] to reduce algebraic multi-valued (MV) operations to binary. In this paper, we explore its potential for a number of problems related to MV SOP minimization, such as computing ISOPs, the set of all primes, and the set of all essential primes. Experimental results show that in some cases these problems can be solved more efficiently than by the traditional MV SOP minimization approaches represented by ESPRESSO-MV, but that generally there is no clear method-of-choice. 1

This paper proposes original algorithms, now integrated in Metaprime, to generate efficiently prime covers, irredundant prime covers, and minimal prime covers of noncoherent fault trees. Experiments show that these algorithms are robust and provide reliability engineers with efficient strategies for the analysis of complex non-coherent multiple-fault trees.