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Given a Boolean formula F(X,Y), where X is a vector of outputs and Y is a vector of inputs, the Boolean functional synthesis problem requires us to compute a Skolem function vector G(Y)for X such that F(G(Y),Y) holds whenever \exists X…
Given a relational specification between Boolean inputs and outputs, the goal of Boolean functional synthesis is to synthesize each output as a function of the inputs such that the specification is met. In this paper, we first show that…
Boolean functional synthesis is the process of constructing a Boolean function from a Boolean specification that relates input and output variables. Despite significant recent developments in synthesis algorithms, Boolean functional…
Given a relational specification between inputs and outputs as a logic formula, the problem of functional synthesis is to automatically synthesize a function from inputs to outputs satisfying the relation. Recently, a rich line of work has…
One approach to probabilistic inference involves counting the number of models of a given Boolean formula. Here, we are interested in inferences involving higher-order objects, i.e., functions. We study the following task: Given a Boolean…
The automated synthesis of correct-by-construction Boolean functions from logical specifications is known as the Boolean Functional Synthesis (BFS) problem. BFS has many application areas that range from software engineering to circuit…
The reactive synthesis problem is to compute a system satisfying a given specification in temporal logic. Bounded synthesis is the approach to bound the maximum size of the system that we accept as a solution to the reactive synthesis…
We present an exact synthesis approach for computing Exclusive-or Sum-of-Products (ESOP) forms with a minimum number of product terms using Boolean satisfiability. Our approach finds one or more ESOP forms for a given Boolean function. The…
Boolean functional synthesis is a fundamental problem in computer science with wide-ranging applications and has witnessed a surge of interest resulting in progressively improved techniques over the past decade. Despite intense algorithmic…
Given a Boolean relational specification between inputs and outputs, the problem of functional synthesis is to construct a function that maps each assignment of the input to an assignment of the output such that each tuple of input and…
Automatic synthesis of hardware components from declarative specifications is an ambitious endeavor in computer aided design. Existing synthesis algorithms are often implemented with Binary Decision Diagrams (BDDs), inheriting their…
Given a Boolean specification between a set of inputs and outputs, the problem of Boolean functional synthesis is to synthesise each output as a function of inputs such that the specification is met. Although the past few years have…
Control Lyapunov functions (CLFs) and control barrier functions (CBFs) are widely used tools for synthesizing controllers subject to stability and safety constraints. Paired with online optimization, they provide stabilizing control actions…
We propose an automatic and formally sound method for synthesising Lyapunov functions for the asymptotic stability of autonomous non-linear systems. Traditional methods are either analytical and require manual effort or are numerical but…
Configurable systems typically consist of reusable assets that have dependencies between each other. To specify such dependencies, feature models are commonly used. As feature models in practice are often complex, automated reasoning is…
A linear pseudo-Boolean constraint (LPB) is an expression of the form $a_1 \cdot \ell_1 + \dots + a_m \cdot \ell_m \geq d$, where each $\ell_i$ is a literal (it assumes the value 1 or 0 depending on whether a propositional variable $x_i$ is…
In the classical synthesis problem, we are given an LTL formula psi over sets of input and output signals, and we synthesize a transducer that realizes psi. One weakness of automated synthesis in practice is that it pays no attention to the…
Boolean function bi-decomposition is ubiquitous in logic synthesis. It entails the decomposition of a Boolean function using two-input simple logic gates. Existing solutions for bi-decomposition are often based on BDDs and, more recently,…
We propose an approach for decomposing Boolean satisfiability problems while extending recent results of \cite{sul2} on solving Boolean systems of equations. Developments in \cite{sul2} were aimed at the expansion of functions $f$ in…
This paper is devoted to the complexity of the Boolean satisfiability problem. We consider a version of this problem, where the Boolean formula is specified in the conjunctive normal form. We prove an unexpected result that the…