Related papers: Pairing Functions, Boolean Evaluation and Binary D…
Logic Programming languages and combinational circuit synthesis tools share a common "combinatorial search over logic formulae" background. This paper attempts to reconnect the two fields with a fresh look at Prolog encodings for the…
For all natural numbers a,b and d > 0, we consider the function f_{a,b,d} which associates n/d to any integer n when it is a multiple of d, and an + b otherwise; in particular f_{3,1,2} is the Collatz function. Coding in base a > 1 with b <…
Parity functions are fundamental Boolean operations with critical applications across machine learning, cryptography, and error correction. Yet, learning high-dimensional parity functions poses significant challenges: in a general setting,…
A symmetric pseudo-Boolean function is a map from Boolean tuples to real numbers which is invariant under input variable interchange. We prove that any such function can be equivalently expressed as a power series or factorized. The kernel…
This paper illustrates the relationship between boolean propositional algebra and semirings, presenting some results of partial ordering on boolean propositional algebras, and the necessary conditions to represent a boolean propositional…
A ProbLog program is a logic program with facts that only hold with a specified probability. In this contribution we extend this ProbLog language by the ability to answer "What if" queries. Intuitively, a ProbLog program defines a…
We consider the problem of jointly minimizing forms of two Boolean functions $f, g \colon \{0,1\}^J \to \{0,1\}$ such that $f + g \leq 1$ and so as to separate disjoint sets $A \cup B \subseteq \{0,1\}^J$ such that $f(A) = \{1\}$ and $g(B)…
We introduce a novel framework, termed $\lambda$DD, that revisits Binary Decision Diagrams from a purely functional point of view. The framework allows to classify the already existing variants, including the most recent ones like Chain-DD…
Consider complex semisimple Lie algebras of a given dimension specified by their structure constants. We describe a finite collection of rational functions in the structure constants that form a complete set of invariants: two sets of…
We present a first result towards the use of entailment in- side relational dual tableau-based decision procedures. To this end, we introduce a fragment of RL(1) which admits a restricted form of composition, (R ; S) or (R ; 1), where the…
Boolean cardinality constraints state that at most (at least, or exactly) $k$ out of $n$ propositional literals can be true. We propose a new class of selection networks that can be used for an efficient encoding of them. Several comparator…
We develop a canonical pairing between trees and graphs, which passes to their quotients by Jacobi identities. This pairing is an effective and simple tool for understanding the Lie and Poisson operads, providing canonical duals. In the…
When using Bayesian networks for modelling the behavior of man-made machinery, it usually happens that a large part of the model is deterministic. For such Bayesian networks deterministic part of the model can be represented as a Boolean…
Based on the partition of parameter space, two algorithms for computing the rational univariate representation of zero-dimensional ideals with parameters are presented in the paper. Unlike the rational univariate representation of…
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…
When modeling real world domains we have to deal with information that is incomplete or that comes from sources with different trust levels. This motivates the need for managing uncertainty in the Semantic Web. To this purpose, we…
In this paper, we mainly investigate profound interconnections between combinatorial designs, linear codes, and Boolean functions.
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…
This paper introduces and analyzes symmetric and anti-symmetric quantum binary functions. Generally, such functions uniquely convert a given computational basis state into a different basis state, but with either a plus or a minus sign.…
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,…