On the complexity of detecting hazards

TL;DR

This paper proves that detecting logic hazards in Boolean circuits is computationally hard under the strong exponential time hypothesis, but provides an efficient algorithm for detecting certain hazards in DNF and CNF formulas.

Contribution

It establishes a complexity lower bound for hazard detection in general circuits and offers a polynomial-time method for specific hazard detection in DNF and CNF formulas.

Findings

No significantly faster algorithm exists for general hazard detection assuming SETH.

Polynomial-time algorithm for detecting 1-hazards in DNF and 0-hazards in CNF.

Practical hazard detection in DNF/CNF formulas is feasible with the proposed method.

Abstract

Detecting and eliminating logic hazards in Boolean circuits is a fundamental problem in logic circuit design. We show that there is no $O(3^{(1-\epsilon)n} \text{poly}(s))$ time algorithm, for any $\epsilon > 0$, that detects logic hazards in Boolean circuits of size $s$ on $n$ variables under the assumption that the strong exponential time hypothesis is true. This lower bound holds even when the input circuits are restricted to be formulas of depth four. We also present a polynomial time algorithm for detecting $1$-hazards in DNF (or, $0$-hazards in CNF) formulas. Since $0$-hazards in DNF (or, $1$-hazards in CNF) formulas are easy to eliminate, this algorithm can be used to detect whether a given DNF or CNF formula has a hazard in practice.