Related papers: Functional Synthesis via Input-Output Separation
Boolean functions can be represented in many ways including logical forms, truth tables, and polynomials. Additionally, Boolean functions have different canonical representations such as minimal disjunctive normal forms. Other canonical…
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…
Decomposition of any Boolean Function BF_n of n binary inputs into an optimal inverter coupled network of Symmetric Boolean functions SF_k (k \leq n) is described. Each SF component is implemented by Threshold Logic Cells, forming a…
Despite many recent advances, reactive synthesis is still not really a practical technique. The grand challenge is to scale from small transition systems, where synthesis performs well, to complex multi-component designs. Compositional…
This paper presents a systematic method for synthesizing a Control Barrier Function (CBF) that encodes predictive information into a CBF. Unlike other methods, the synthesized CBF can account for changes and time-variations in the…
Given a CNF formula $F$, we present a new algorithm for deciding the satisfiability (SAT) of $F$ and computing all solutions of assignments. The algorithm is based on the concept of \emph{cofactors} known in the literature. This paper is a…
We study LTLf synthesis with multiple properties, where satisfying all properties may be impossible. Instead of enumerating subsets of properties, we compute in one fixed-point computation the relation between product-game states and the…
Program Synthesis is the mapping of a specification of what a computer program is supposed to do, into a computer program that does what the specification says to do. This is equivalent to constructing any computer program and a sound proof…
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…
Component-based synthesis seeks to build programs using the APIs provided by a set of libraries. Oftentimes, these APIs have effects, which make it challenging to reason about the correctness of potential synthesis candidates. This is…
Given a Linear Temporal Logic (LTL) formula over input and output variables, reactive synthesis requires us to design a deterministic Mealy machine that gives the values of outputs at every time step for every sequence of inputs, such that…
Functional ANOVA offers a principled framework for interpretability by decomposing a model's prediction into main effects and higher-order interactions. For independent features, this decomposition is well-defined, strongly linked with SHAP…
A quantum single-error-correcting scheme can be derived from a one-way entanglement purification protocol in purifying one Bell state from a finite block of five Bell states. The main issue to be concerned with in the theory of such an…
This is the latest in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. In the previous papers, we have proved that the sat CNF problem is polynomially reduced to the problem of finding a…
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…
This paper proposes an algorithm for deciding consistency of systems of Boolean equations in several variables with co-efficients in the two element Boolean algebra $B_{0}=\{0,1\}$ and find all satisfying assignments. The algorithm is based…
This paper develops a parallel computational solver for computing all satifying assignments of a Boolean system of equations defined by Boolean functions of several variables. While there are we known solvers for satisfiability of Boolean…
A Pseudo-Boolean (PB) constraint is a linear arithmetic constraint over Boolean variables. PB constraints are convenient and widely used in expressing NP-complete problems. We introduce a new, two step, method for transforming PB…
Reversible Boolean function is a one-to-one function which maps $n$-bit input to $n$-bit output. Reversible logic synthesis has been widely studied due to its relationship with low-energy computation as well as quantum computation. In this…
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…