A Logic Programming Framework for Combinational Circuit Synthesis

TL;DR

This paper presents a logic programming approach using Prolog for efficient combinational circuit synthesis, leveraging parallel bitstring operations and a novel library comparison to optimize circuit design.

Contribution

It introduces a Prolog-based framework with parallel bitstring operations for circuit synthesis and compares minimal logic libraries, revealing surprising efficiencies.

Findings

Strict Boolean Inequality '<' with constant '1' is a competitive minimal library.

The framework achieves efficient exhaustive search for circuit synthesis.

Rewriting-based simplification improves circuit optimization.

Abstract

Logic Programming languages and combinational circuit synthesis tools share a common "combinatorial search over logic formulae" background. This paper attempts to reconnect the two fields with a fresh look at Prolog encodings for the combinatorial objects involved in circuit synthesis. While benefiting from Prolog's fast unification algorithm and built-in backtracking mechanism, efficiency of our search algorithm is ensured by using parallel bitstring operations together with logic variable equality propagation, as a mapping mechanism from primary inputs to the leaves of candidate Leaf-DAGs implementing a combinational circuit specification. After an exhaustive expressiveness comparison of various minimal libraries, a surprising first-runner, Strict Boolean Inequality "<" together with constant function "1" also turns out to have small transistor-count implementations, competitive to NAND-only or NOR-only libraries. As a practical outcome, a more realistic circuit synthesizer is implemented that combines rewriting-based simplification of (<,1) circuits with exhaustive Leaf-DAG circuit search. Keywords: logic programming and circuit design, combinatorial object generation, exact combinational circuit synthesis, universal boolean logic libraries, symbolic rewriting, minimal transistor-count circuit synthesis