A recursive paradigm to solve Boolean relations

A Boolean relation can specify some types of flexibility of a combinational circuit that cannot be expressed with don't cares. Several problems in logic synthesis, such as Boolean decomposition or multilevel minimization, can be modeled with Boolean relations. However, solving Boolean relations is a computationally expensive task. This paper presents a novel recursive algorithm for solving Boolean relations. The algorithm has several features: efficiency, wide exploration of solutions, and customizable cost function. The experimental results show the applicability of the method in logic minimization problems and tangible improvements with regard to previous heuristic approaches

Logic Synthesis as an Efficient Means of Minimal Model Discovery from Multivariable Medical Datasets

In this paper we review the application of logic synthesis methods for uncovering minimal structures in observational/medical datasets. Traditionally used in digital circuit design, logic synthesis has taken major strides in the past few decades and forms the foundation of some of the most powerful concepts in computer science and data mining. Here we provide a review of current state of research in application of logic synthesis methods for data analysis and provide a demonstrative example for systematic application and reasoning based on these methods

Fast Heuristic and Exact Algorithms for Two-Level Hazard-Free Logic Minimization

None of the available minimizers for 2-level hazard-free logic minimization can synthesize very large circuits. This limitation has forced researchers to resort to manual and automated circuit partitioning techniques. This paper introduces two new 2-level logic minimizers:ESPRESSO-HF, a heuristic method which is loosely based on ESPRESSO-II, and IMPYMIN, an exact method based on implicit data structures. Both minimizers can solve all currently available examples, which range up to 32 inputs and 33 outputs.These include examples that have never been solved before.For examples that can be solved by other minimizers our methods are several orders of magnitude faster. As by-products of these algorithms, we also present two additional results. First, we introduce a fast new algorithm to check if a hazard-free covering problem can feasibly be solved. Second, we introduce a novel formulation of the 2-level hazard-free logic minimization problem by capturing hazard-freedom constraints within a synchronous function by adding new variables

Fast Heuristic and Exact Algorithms for Two-Level Hazard-Free Logic Minimization

None of the available minimizers for 2-level hazard-free logic minimization can synthesize very large circuits. This limitation has forced researchers to resort to manual and automated circuit partitioning techniques. This paper introduces two new 2-level logic minimizers:ESPRESSO-HF, a heuristic method which is loosely based on ESPRESSO-II, and IMPYMIN, an exact method based on implicit data structures. Both minimizers can solve all currently available examples, which range up to 32 inputs and 33 outputs.These include examples that have never been solved before.For examples that can be solved by other minimizers our methods are several orders of magnitude faster. As by-products of these algorithms, we also present two additional results. First, we introduce a fast new algorithm to check if a hazard-free covering problem can feasibly be solved. Second, we introduce a novel formulation of the 2-level hazard-free logic minimization problem by capturing hazard-freedom constraints within a synchronous function by adding new variables

Smooth and Strong PCPs

Probabilistically checkable proofs (PCPs) can be verified based only on a constant amount of random queries, such that any correct claim has a proof that is always accepted, and incorrect claims are rejected with high probability (regardless of the given alleged proof). We consider two possible features of PCPs: - A PCP is strong if it rejects an alleged proof of a correct claim with probability proportional to its distance from some correct proof of that claim. - A PCP is smooth if each location in a proof is queried with equal probability. We prove that all sets in NP have PCPs that are both smooth and strong, are of polynomial length, and can be verified based on a constant number of queries. This is achieved by following the proof of the PCP theorem of Arora, Lund, Motwani, Sudan and Szegedy (JACM, 1998), providing a stronger analysis of the Hadamard and Reed - Muller based PCPs and a refined PCP composition theorem. In fact, we show that any set in NP has a smooth strong canonical PCP of Proximity (PCPP), meaning that there is an efficiently computable bijection of NP witnesses to correct proofs. This improves on the recent construction of Dinur, Gur and Goldreich (ITCS, 2019) of PCPPs that are strong canonical but inherently non-smooth. Our result implies the hardness of approximating the satisfiability of "stable" 3CNF formulae with bounded variable occurrence, where stable means that the number of clauses violated by an assignment is proportional to its distance from a satisfying assignment (in the relative Hamming metric). This proves a hypothesis used in the work of Friggstad, Khodamoradi and Salavatipour (SODA, 2019), suggesting a connection between the hardness of these instances and other stable optimization problems