Related papers: Testing Formula Satisfaction
We give a unateness tester for functions of the form $f:[n]^d\rightarrow R$, where $n,d\in \mathbb{N}$ and $R\subseteq \mathbb{R}$ with query complexity $O(\frac{d\log (\max(d,n))}{\epsilon})$. Previously known unateness testers work only…
We study -- within the framework of propositional proof complexity -- the problem of certifying unsatisfiability of CNF formulas under the promise that any satisfiable formula has many satisfying assignments, where ``many'' stands for an…
This paper explores a fine-grained version of the Watrous conjecture, including the randomized and quantum algorithms with success probabilities arbitrarily close to $1/2$. Our contributions include the following: i) An analysis of the…
Given Boolean functions \( f, g : \mathbb{F}_2^n \to \{-1,+1\} \), we say they are {\em linearly isomorphic} if there exists \( A \in \mathrm{GL}_n(\mathbb{F}_2) \) such that \( f(x)=g(Ax) \) for all \( x \). We study this problem in the…
We consider the task of testing properties of Boolean functions that are invariant under linear transformations of the Boolean cube. Previous work in property testing, including the linearity test and the test for Reed-Muller codes, has…
Let $f$ and $g$ be Boolean functions over a finite Abelian group $\mathcal{G}$, where $g$ is fully known, and we have {\em query access} to $f$, that is, given any $x \in \mathcal{G}$ we can get the value $f(x)$. We study the tolerant…
Completeness is a desirable property of test suites. Roughly, completeness guarantees that a non-equivalent implementation under test will always be identified. Several approaches proposed sufficient, and sometimes also necessary,…
This paper shows that the problem of testing hypotheses in moment condition models without any assumptions about identification may be considered as a problem of testing with an infinite-dimensional nuisance parameter. We introduce a…
In the paper, we consider several types of queries for classical and new problems of learning and testing read-once functions. In several cases, the border between polynomial and exponential complexities is obtained.
We study unitary property testing, where a quantum algorithm is given query access to a black-box unitary and has to decide whether it satisfies some property. In addition to containing the standard quantum query complexity model (where the…
Satisfiability of Boolean circuits is among the most known and important problems in theoretical computer science. This problem is NP-complete in general but becomes polynomial time when restricted either to monotone gates or linear gates.…
Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact,…
We study the Boolean Satisfiability problem (SAT) in the framework of diversity, where one asks for multiple solutions that are mutually far apart (i.e., sufficiently dissimilar from each other) for a suitable notion of…
In this paper, we study learning and testing decision tree of size and depth that are significantly smaller than the number of attributes $n$. Our main result addresses the problem of poly$(n,1/\epsilon)$ time algorithms with…
The framework of distribution testing is currently ubiquitous in the field of property testing. In this model, the input is a probability distribution accessible via independently drawn samples from an oracle. The testing task is to…
We present simple, self-contained proofs of correctness for algorithms for linearity testing and program checking of linear functions on finite subsets of integers represented as n-bit numbers. In addition we explore a generalization of…
In this paper we initiate the study of \emph{property testing of weighted computational networks viewed as computational devices}. Our goal is to design property testing algorithms that for a given computational network with oracle access…
In this paper, based on results of exact learning and test theory, we study arbitrary infinite binary information systems each of which consists of an infinite set of elements and an infinite set of two-valued functions (attributes) defined…
We study a well-known technique of using absoluteness for giving choice-free proofs to some statements which are known to be provable with the axiom of choice. The idea is to reduce the problem to an inner model where the axiom of choice…
The proof of a program property can be reduced to the proof of satisfiability of a set of constrained Horn clauses (CHCs) which can be automatically generated from the program and the property. In this paper we have conducted a case study…