Related papers: What's hard about Boolean Functional Synthesis
The nonlinearity of a Boolean function is a key property in deciding its suitability for cryptographic purposes, e.g. as a combining function in stream ciphers, and so the nonlinearity computation is an important problem for applications.…
When writing programs, people have the ability to tackle a new complex task by decomposing it into smaller and more familiar subtasks. While it is difficult to measure whether neural program synthesis methods have similar capabilities, what…
The automatic generation of computer programs is one of the main applications with practical relevance in the field of evolutionary computation. With program synthesis techniques not only software developers could be supported in their…
An important issue with oversampled FIR analysis filter banks (FBs) is to determine inverse synthesis FBs, when they exist. Given any complex oversampled FIR analysis FB, we first provide an algorithm to determine whether there exists an…
In component-based program synthesis, the synthesizer generates a program given a library of components (functions). Existing component-based synthesizers have difficulty synthesizing loops and other control structures, and they often…
The hidden shift problem is a natural place to look for new separations between classical and quantum models of computation. One advantage of this problem is its flexibility, since it can be defined for a whole range of functions and a…
Symbolic controller synthesis is a fully-automated and correct-by-design synthesis scheme whose limitations are its immense memory and runtime requirements. A current trend to compensate for this downside is to develop techniques for…
Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where…
Time-varying optimization is fundamental to decision-making in dynamic environments, where objectives evolve over time due to exogenous signals or data streams. However, algorithms designed for static problems yield suboptimal decisions in…
Determining the approximate degree composition for Boolean functions remains a significant unsolved problem in Boolean function complexity. In recent decades, researchers have concentrated on proving that approximate degree composes for…
Large language models (LLMs) have enabled a range of applications in zero-shot and few-shot learning settings, including the generation of synthetic datasets for training and testing. However, to reliably use these synthetic datasets, it is…
Extending previous analyses on function classes like linear functions, we analyze how the simple (1+1) evolutionary algorithm optimizes pseudo-Boolean functions that are strictly monotone. Contrary to what one would expect, not all of these…
Boolean Matrix Factorization (BMF) aims to find an approximation of a given binary matrix as the Boolean product of two low-rank binary matrices. Binary data is ubiquitous in many fields, and representing data by binary matrices is common…
The Boolean Satisfiability (SAT) problem is the canonical NP-complete problem and is fundamental to computer science, with a wide array of applications in planning, verification, and theorem proving. Developing and evaluating practical SAT…
Attempts to separate the power of classical and quantum models of computation have a long history. The ultimate goal is to find exponential separations for computational problems. However, such separations do not come a dime a dozen: while…
In recent years, deep learning techniques have been developed to improve the performance of program synthesis from input-output examples. Albeit its significant progress, the programs that can be synthesized by state-of-the-art approaches…
We consider a system consisting of a sequential composition of Mealy machines, called head and tail. We study two problems related to these systems. In the first problem, models of both head and tail components are available, and the aim is…
LTL synthesis is the problem of synthesizing a reactive system from a formal specification in Linear Temporal Logic. The extension of allowing for partial observability, where the system does not have direct access to all relevant…
The discovery of functional molecules is an expensive and time-consuming process, exemplified by the rising costs of small molecule therapeutic discovery. One class of techniques of growing interest for early-stage drug discovery is de novo…
The subject of this textbook is the analysis of Boolean functions. Roughly speaking, this refers to studying Boolean functions $f : \{0,1\}^n \to \{0,1\}$ via their Fourier expansion and other analytic means. Boolean functions are perhaps…