Related papers: Knowledge Compilation for Boolean Functional Synth…
Symbolic Mathematical tasks such as integration often require multiple well-defined steps and understanding of sub-tasks to reach a solution. To understand Transformers' abilities in such tasks in a fine-grained manner, we deviate from…
We introduce DafnyCOMP, a benchmark for evaluating large language models (LLMs) on compositional specification generation in Dafny. Unlike prior benchmarks that focus on single-function tasks, DafnyCOMP targets programs composed of multiple…
We prove two new results about the randomized query complexity of composed functions. First, we show that the randomized composition conjecture is false: there are families of partial Boolean functions $f$ and $g$ such that $R(f\circ g)\ll…
A well-studied class of functions in communication complexity are composed functions of the form $(f \comp g^n)(x,y)=f(g(x^1, y^1),..., g(x^n,y^n))$. This is a rich family of functions which encompasses many of the important examples in the…
Structured $d$-DNNFs and SDDs are restricted negation normal form circuits used in knowledge compilation as target languages into which propositional theories are compiled. Structuredness is imposed by so-called vtrees. By definition SDDs…
Knowledge compilation studies the trade-off between succinctness and efficiency of different representation languages. For many languages, there are known strong lower bounds on the representation size, but recent work shows that, for some…
Let the randomized query complexity of a relation for error probability $\epsilon$ be denoted by $R_\epsilon(\cdot)$. We prove that for any relation $f \subseteq \{0,1\}^n \times \mathcal{R}$ and Boolean function $g:\{0,1\}^m \rightarrow…
Schaefer's theorem is a complexity classification result for so-called Boolean constraint satisfaction problems: it states that every Boolean constraint satisfaction problem is either contained in one out of six classes and can be solved in…
Since its introduction by Valiant in 1984, PAC learning of DNF expressions remains one of the central problems in learning theory. We consider this problem in the setting where the underlying distribution is uniform, or more generally, a…
Inspired by recent progress in dynamic programming approaches for weighted model counting, we investigate a dynamic-programming approach in the context of boolean realizability and synthesis, which takes a conjunctive-normal-form boolean…
A major problem in computational learning theory is whether the class of formulas in conjunctive normal form (CNF) is efficiently learnable. Although it is known that this class cannot be polynomially learned using either membership or…
Program synthesis is challenging largely because of the difficulty of search in a large space of programs. Human programmers routinely tackle the task of writing complex programs by writing sub-programs and then analyzing their intermediate…
The aim of the paper is to answer a long-standing open problem on the relationship between NP and BQP. The paper shows that BQP contains NP by proposing a BQP quantum algorithm for the MAX-E3-SAT problem which is a fundamental NP-hard…
Suppose $\XX{N}$ is a uniformly distributed $N$-dimensional binary vector and $\YY{N}$ is obtained by passing $\XX{N}$ through a binary symmetric channel with crossover probability $\alpha$. Recently, Courtade and Kumar postulates that…
Python type inference is challenging in practice. Due to its dynamic properties and extensive dependencies on third-party libraries without type annotations, the performance of traditional static analysis techniques is limited. Although…
LTLf synthesis is the process of finding a strategy that satisfies a linear temporal specification over finite traces. An existing solution to this problem relies on a reduction to a DFA game. In this paper, we propose a symbolic framework…
The control Lyapunov function (CLF) approach to nonlinear control design is well established. Moreover, when the plant is control affine and polynomial, sum-of-squares (SOS) optimization can be used to find a polynomial controller as a…
Here, in a series of articles, we show methods for calculating propositional statements using algebraic polynomials as symbols for the connectives, which are named operators. These polynomials originate from the transformation between the…
We propose a perspective on knowledge compilation which calls for analyzing different compilation approaches according to two key dimensions: the succinctness of the target compilation language, and the class of queries and transformations…
We consider the problem of computing the Boolean convolution (with wraparound) of $n$~vectors of dimension $m$, or, equivalently, the problem of computing the sumset $A_1+A_2+\ldots+A_n$ for $A_1,\ldots,A_n \subseteq \mathbb{Z}_m$. Boolean…