Related papers: Testing Formula Satisfaction
The field of property testing of probability distributions, or distribution testing, aims to provide fast and (most likely) correct answers to questions pertaining to specific aspects of very large datasets. In this work, we consider a…
The main reason for query model's prominence in complexity theory and quantum computing is the presence of concrete lower bounding techniques: polynomial and adversary method. There have been considerable efforts to give lower bounds using…
An \emph{arithmetic read-once formula} (ROF for short) is a formula (i.e. a tree of computation) in which the operations are $\{+,\times\}$ and such that every input variable labels at most one leaf. We give a simple characterization of…
We describe a $\tilde{O}(d^{5/6})$-query monotonicity tester for Boolean functions $f:[n]^d \to \{0,1\}$ on the $n$-hypergrid. This is the first $o(d)$ monotonicity tester with query complexity independent of $n$. Motivated by this…
A language L has a property tester if there exists a probabilistic algorithm that given an input x only asks a small number of bits of x and distinguishes the cases as to whether x is in L and x has large Hamming distance from all y in L.…
In this paper, we study classes of Boolean functions that are testable with $O(\psi+1/\epsilon)$ queries, where $\psi$ depends on the parameters of the class (e.g., the number of terms, the number of relevant variables, etc.) but not on the…
The Boolean satisfiability problem (SAT) is a well-known example of monotonic reasoning, of intense practical interest due to fast solvers, complemented by rigorous fine-grained complexity results. However, for non-monotonic reasoning,…
A unary constraint (on the Boolean domain) is a function from {0,1} to the set of real numbers. A free use of auxiliary unary constraints given besides input instances has proven to be useful in establishing a complete classification of the…
This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in…
Let $\mathcal{P}$ be a property of function $\mathbb{F}_p^n \to \{0,1\}$ for a fixed prime $p$. An algorithm is called a tester for $\mathcal{P}$ if, given a query access to the input function $f$, with high probability, it accepts when $f$…
We initiate the study of parameterized complexity of $\textsf{QMA}$ problems in terms of the number of non-Clifford gates in the problem description. We show that for the problem of parameterized quantum circuit satisfiability, there exists…
This paper studies the problem of testing if an input (Gamma,*), where Gamma is a finite set of unknown size and * is a binary operation over Gamma given as an oracle, is close to a specified class of groups. Friedl et al. [Efficient…
In this expository paper we describe four primality tests. The first test is very efficient, but is only capable of proving that a given number is either composite or 'very probably' prime. The second test is a deterministic polynomial time…
We prove a lower bound of $\tilde{\Omega}(n^{1/3})$ for the query complexity of any two-sided and adaptive algorithm that tests whether an unknown Boolean function $f:\{0,1\}^n\rightarrow \{0,1\}$ is monotone or far from monotone. This…
Runtime Verification deals with the question of whether a run of a system adheres to its specification. This paper studies runtime verification in the presence of partial knowledge about the observed run, particularly where input values may…
Boolean satisfiability problem has applications in various fields. An efficient algorithm to solve satisfiability problem can be used to solve many other problems efficiently. The input of satisfiability problem is a finite set of clauses.…
For typical first-order logical theories, satisfying assignments have a straightforward finite representation that can directly serve as a certificate that a given assignment satisfies the given formula. For non-linear real arithmetic…
A preferential domain is a collection of sets of preferences which are linear orders over a set of alternatives. These domains have been studied extensively in social choice theory due to both its practical importance and theoretical…
A test of quantumness is a protocol that allows a classical verifier to certify (only) that a prover is not classical. We show that tests of quantumness that follow a certain template, which captures recent proposals such as (Kalai et al.,…
The Huge Object model of property testing [Goldreich and Ron, TheoretiCS 23] concerns properties of distributions supported on $\{0,1\}^n$, where $n$ is so large that even reading a single sampled string is unrealistic. Instead, query…