Related papers: Checking Tests for Read-Once Functions over Arbitr…
In this paper, we analyze 2CNF formulas from the perspectives of Read-Once resolution (ROR) refutation schemes. We focus on two types of ROR refutations, viz., variable-once refutation and clause-once refutation. In the former, each…
For every $n >0$, we show the existence of a CNF tautology over $O(n^2)$ variables of width $O(\log n)$ such that it has a Polynomial Calculus Resolution refutation over $\{0,1\}$ variables of size $O(n^3polylog(n))$ but any Polynomial…
Our problem is to evaluate a multi-valued Boolean function $F$ through oracle calls. If $F$ is one-to-one and the size of its domain and range is the same, then our problem can be formulated as follows: Given an oracle $f(a,x):…
We extend first-order logic to include variadic function symbols, and prove a substitution lemma. Two applications are given: one to bounded quantifier elimination and one to the definability of certain Borel sets.
We consider the Stochastic Boolean Function Evaluation (SBFE) problem in the well-studied case of $k$-of-$n$ functions: There are independent Boolean random variables $x_1,\dots,x_n$ where each variable $i$ has a known probability $p_i$ of…
Recognizing, quantifying and visualizing associations between two variables is increasingly important. This paper investigates how a new function-valued measure of dependence, the quantile dependence function, can be used to construct tests…
We show that there exists a Boolean function $F$ which observes the following separations among deterministic query complexity $(D(F))$, randomized zero error query complexity $(R_0(F))$ and randomized one-sided error query complexity…
We study a class of hypothesis testing problems in which, upon observing the realization of an $n$-dimensional Gaussian vector, one has to decide whether the vector was drawn from a standard normal distribution or, alternatively, whether…
Scientific theories can often be formulated using equality and order constraints on the relative effects in a linear regression model. For example, it may be expected that the effect of the first predictor is larger than the effect of the…
Checking the semantic equivalence of operations is an important task in software development. For instance, regression testing is a routine task performed when software systems are developed and improved, and software package managers…
Concolic testing is a popular dynamic validation technique that can be used for both model checking and automatic test case generation. We have recently introduced concolic testing in the context of logic programming. In contrast to…
Off-policy evaluation in reinforcement learning offers the chance of using observational data to improve future outcomes in domains such as healthcare and education, but safe deployment in high stakes settings requires ways of assessing its…
We study the problem of evaluating a discrete function by adaptively querying the values of its variables until the values read uniquely determine the value of the function. Reading the value of a variable is done at the expense of some…
Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…
We prove that $1-o(1)$ fraction of all $k$-SAT functions on $n$ Boolean variables are unate (i.e., monotone after first negating some variables), for any fixed positive integer $k$ and as $n \to \infty$. This resolves a conjecture by…
By using a new way to encode Boolean functions in a reversible gate, an algorithm is developed in quantum computing over Z_2, symbolized QC/2, (as opposed to QC over C) that needs only one function evaluation to solve the Grover Database…
Let $n$ be a positive integer and $f$ a differentiable function from a convex subset $C$ of the Euclidean space $\mathbb{R}^n$ to a smooth manifold. We define an invariant of $f$ via counting certain threshold functions associated to $f$.…
There have been two different methods for checking the satisfiability of feature descriptions that use the functional uncertainty device, namely~\cite{Kaplan:88CO} and \cite{Backofen:94JSC}. Although only the one in \cite{Backofen:94JSC}…
To support reasoning about properties of programs operating with boolean values one needs theorem provers to be able to natively deal with the boolean sort. This way, program properties can be translated to first-order logic and theorem…
The forcing theorem is the most fundamental result about set forcing, stating that the forcing relation for any set forcing is definable and that the truth lemma holds, that is everything that holds in a generic extension is forced by a…