Related papers: Exact Synthesis of ESOP Forms
This is the second in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. The research in this article aims to find conditions of an algorithmic nature that are necessary and sufficient to…
The Pseudo-Boolean Optimization (PBO) and Maximum Satisfiability (MaxSAT) problems are natural optimization extensions of Boolean Satisfiability (SAT). In the recent past, different algorithms have been proposed for PBO and for MaxSAT,…
Boolean Satisfiability (SAT) problems are critical in fields such as artificial intelligence and cryptography, where efficient solutions are essential. Conventional probabilistic solvers often encounter scalability issues due to complex…
A finite sum of exponential functions may be expressed by a linear combination of powers of the independent variable and by successive integrals of the sum. This is proved for the general case and the connection between the parameters in…
This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…
Visual grouping -- operationalized through tasks such as instance segmentation, visual grounding, and object detection -- enables applications ranging from robotic perception to photo editing. These fundamental problems in computer vision…
We develop exact simulation (also known as perfect sampling) algorithms for a family of assemble-to-order systems. Due to the finite capacity, and coupling in demands and replenishments, known solving techniques are inefficient for larger…
We present a method for the synthesis of polynomial lasso programs. These programs consist of a program stem, a set of transitions, and an exit condition, all in the form of algebraic assertions (conjunctions of polynomial equalities).…
We give a new general approach for designing exact exponential-time algorithms for subset problems. In a subset problem the input implicitly describes a family of sets over a universe of size n and the task is to determine whether the…
Symmetries are intrinsic to many combinatorial problems including Boolean Satisfiability (SAT) and Constraint Programming (CP). In SAT, the identification of symmetry breaking predicates (SBPs) is a well-known, often effective, technique…
Submodular function minimization is a key problem in a wide variety of applications in machine learning, economics, game theory, computer vision, and many others. The general solver has a complexity of $O(n^3 \log^2 n . E +n^4 {\log}^{O(1)}…
We present a novel algorithm that synthesizes imperative programs for introductory programming courses. Given a set of input-output examples and a partial program, our algorithm generates a complete program that is consistent with every…
Boolean symbolic reasoning for gate-level netlists is a critical step in verification, logic and datapath synthesis, and hardware security. Specifically, reasoning datapath and adder tree in bit-blasted Boolean networks is particularly…
Although Boolean Constraint Technology has made tremendous progress over the last decade, the efficacy of state-of-the-art solvers is known to vary considerably across different types of problem instances and is known to depend strongly on…
We explore and formalize the task of synthesizing programs over noisy data, i.e., data that may contain corrupted input-output examples. By formalizing the concept of a Noise Source, an Input Source, and a prior distribution over programs,…
Much effort is spent everyday by programmers in trying to reduce long, failing execution traces to the cause of the error. We present a new algorithm for error cause localization based on a reduction to the maximal satisfiability problem…
Two contrasting algorithmic paradigms for constraint satisfaction problems are successive local explorations of neighboring configurations versus producing new configurations using global information about the problem (e.g. approximating…
A key challenge in program synthesis is the astronomical size of the search space the synthesizer has to explore. In response to this challenge, recent work proposed to guide synthesis using learned probabilistic models. Obtaining such a…
We present several families of total boolean functions which have exact quantum query complexity which is a constant multiple (between 1/2 and 2/3) of their classical query complexity, and show that optimal quantum algorithms for these…
The sparsity of natural signals and images in a transform domain or dictionary has been extensively exploited in several applications such as compression, denoising and inverse problems. More recently, data-driven adaptation of synthesis…