Proof. SAT is in NP (easy). To prove NP-hardness, we will show that Circuit-SAT is reducible to SAT. Let C be an arbitrary Boolean circuit with gates g1, . . . , gm, where g1, . . . , gn are input gates and gm is the output gate. For each gj, introduce a Boolean variable yj. For every i > n, define the Boolean formula gatei expressing that the value of yi is equal to the value of the gate gi. T...

We present a characterization of short-term stability of Kauffman's NK (random) Boolean networks under arbitrary distributions of transfer functions. Given such a Boolean network where each transfer function is drawn from the same distribution, we present a formula that determines whether short-term chaos (damage spreading) will happen. Our main technical tool which enables the formal proof of ...

Pseudo-Boolean constraints, also known as 0-1 Integer Linear Constraints, are used to model many real-world problems. A common approach to solve these constraints is to encode them into a SAT formula. The runtime of the SAT solver on such formula is sensitive to the manner in which the given pseudo-Boolean constraints are encoded. In this paper, we propose generalized Totalizer encoding (GTE), ...

This paper presents, for the first time, a Geometry of Interaction (GoI) interpretation using Hughes-vanGlabbeek (HvG) proof-nets for multiplicative additive linear logic (MALL). Our GoI captures dynamically HvG’s geometric correctness criterion–the toggling cycle condition–in terms of algebraic operators. Our new ingredient is a scalar extension of the *-algebra in Girard’s *-ring of partial i...

Static verification techniques leverage Boolean formula satisfiability solvers such as SAT and SMT solvers that operate on conjunctive normal form and first order logic formulae, respectively, to validate programs. They force bounds on variable ranges and execution time and translate the program and its specifications into a Boolean formula. They are limited to programs of relatively low comple...

A {formula is a Boolean formula in which each variable occurs at most once. The paper treats its molecular representation including its queries using techniques in molecular biology. The novelty is that this method can evaluate a Boolean formula in a single tube within a short time. The preliminary experimental result suggests the possibility of parallel evaluation and learning of general {form...

We show that any monotone linear threshold function on n Boolean variables can be approximated to within any constant accuracy by a monotone Boolean formula of poly(n) size.

The following problem is considered: given a Boolean formula f, generate another formula g such that: (i) If f is unsatisfiable then g is also unsatisfiable. (ii) If f is satisfiable then g is also satisfiable and furthermore g is “easier” than f. For the measure of this easiness, we use the density of a formula f which is defined as (the number of satisfying assignments)/2n, where n is the num...

We investigate the relationship between the directional and the undirectional complexity of read-once Boolean formulas on the randomized decision tree model. It was known that there is a read-once Boolean formula such that an optimal randomized algorithm to evaluate it is not directional. This was first pointed out by Saks and Wigderson (1986) and an explicit construction of such a formula was ...

Models of biochemical networks are frequently complex and high-dimensional. Reduction methods that preserve important dynamical properties are therefore essential for their study. Interactions in biochemical networks are frequently modeled using Hill functions ([Formula: see text]). Reduced ODEs and Boolean approximations of such model networks have been studied extensively when the exponent [F...