Related papers: Functional Synthesis via Input-Output Separation
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
Automated Verilog code synthesis poses significant challenges and typically demands expert oversight. Traditional high-level synthesis (HLS) methods often fail to scale for real-world designs. While large language models (LLMs) have…
Program synthesis from incomplete specifications (e.g. input-output examples) has gained popularity and found real-world applications, primarily due to its ease-of-use. Since this technology is often used in an interactive setting,…
Analyzing a Feature Model (FM) and reasoning on the corresponding configuration space is a central task in Software Product Line (SPL) engineering. Problems such as deciding the satisfiability of the FM and eliminating inconsistent parts of…
Efficient characteristic set methods for computing solutions of polynomial equation systems in a finite field are proposed. The concept of proper triangular sets is introduced and an explicit formula for the number of solutions of a proper…
In this work, we employ the concept of {\em composite representation} of Boolean functions, which represents an arbitrary Boolean function as a composition of one Boolean function and one vectorial function, for the purpose of specifying…
A long-investigated problem in circuit complexity theory is to decompose an $n$-input or $n$-variable Majority Boolean function (call it $M_n$) using $k$-input ones ($M_k$), $k < n$, where the objective is to achieve the decomposition using…
In this report, we propose a quick survey of the currently known techniques for encoding a Boolean cardinality constraint into a CNF formula, and we discuss about the relevance of these encodings. We also propose models to facilitate…
$\newcommand{\EC}{\mathsf{EC}}\newcommand{\KW}{\mathsf{KW}}\newcommand{\DT}{\mathsf{DT}}\newcommand{\psens}{\mathsf{psens}} \newcommand{\calB}{{\cal B}} $ For a Boolean function $f:\{0,1\}^n \to \{0,1\}$ computed by a circuit $C$ over a…
Boolean functions and networks are commonly used in the modeling and analysis of complex biological systems, and this paradigm is highly relevant in other important areas in data science and decision making, such as in the medical field and…
This paper presents a new approach for guaranteed safety subject to input constraints (e.g., actuator limits) using a composition of multiple control barrier functions (CBFs). First, we present a method for constructing a single CBF from…
Stochastic Boolean Function Evaluation (SBFE) is the problem of determining the value of a given Boolean function $f$ on an unknown input $x$, when each bit of $x_i$ of $x$ can only be determined by paying a given associated cost $c_i$.…
Early stages of system development involve outlining desired features such as functionality, availability, or usability. Specifications are derived from these features that concretize vague ideas presented in natural languages. The…
Synthesis is the automatic construction of a system from its specification. In classical synthesis algorithms it is always assumed that the system is "constructed from scratch" rather than composed from reusable components. This, of course,…
Given a specification $\varphi(X,Y)$ over inputs $X$ and output $Y$, defined over a background theory $\mathbb{T}$, the problem of program synthesis is to design a program $f$ such that $Y=f(X)$ satisfies the specification $\varphi$. Over…
The increasing automation in many areas of the Industry expressly demands to design efficient machine-learning solutions for the detection of abnormal events. With the ubiquitous deployment of sensors monitoring nearly continuously the…
A novel approach for structure alignment is presented, where the key ingredients are: (1) An error function formulation of the problem simultaneously in terms of binary (Potts) assignment variables and real-valued atomic coordinates. (2)…
The paper studies machine learning problems where each example is described using a set of Boolean features and where hypotheses are represented by linear threshold elements. One method of increasing the expressiveness of learned hypotheses…
In this article, we continue our study on universal learning machine by introducing new tools. We first discuss boolean function and boolean circuit, and we establish one set of tools, namely, fitting extremum and proper sampling set. We…
We propose a framework for synthesizing inductive invariants for incomplete verification engines, which soundly reduce logical problems in undecidable theories to decidable theories. Our framework is based on the counter-example guided…