Related papers: Language of Boolean functions its Grammar and Mach…
We develop Boolean-valued domain theory and show how the lambda-calculus can be interpreted in using domain-valued random variables. We focus on the reflexive domain construction rather than the language and its semantics. The notion of…
This short note reviews briefly three algorithms for finding the set of dispensable variables of a boolean formula. The presentation is light on proofs and heavy on intuitions.
Boolean functions are mathematical objects used in diverse domains and have been actively researched for several decades already. One domain where Boolean functions play an important role is cryptography. There, the plethora of settings one…
We study the space of functions computed by random-layered machines, including deep neural networks and Boolean circuits. Investigating the distribution of Boolean functions computed on the recurrent and layer-dependent architectures, we…
Recent years have witnessed a renewed interest in Boolean function in explaining binary classifiers in the field of explainable AI (XAI). The standard approach of Boolean function is propositional logic. We present a modal language of a…
We propose a unified neural network architecture and learning algorithm that can be applied to various natural language processing tasks including: part-of-speech tagging, chunking, named entity recognition, and semantic role labeling. This…
A solution is proposed for the problem of composition of ordinary generating functions. A new class of functions that provides a composition of ordinary generating functions is introduced; main theorems are presented; compositae are written…
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…
Mapping functions on bits to Hamiltonians acting on qubits has many applications in quantum computing. In particular, Hamiltonians representing Boolean functions are required for applications of quantum annealing or the quantum approximate…
This paper is concerned with a class of algorithms that perform exhaustive search on propositional knowledge bases. We show that each of these algorithms defines and generates a propositional language. Specifically, we show that the trace…
Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box and the aim is to compute function value for arbitrary input using as few queries as possible. We concentrate on quantum…
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…
This paper presents a currently bilingual but potentially multilingual FrameNet-based grammar library implemented in Grammatical Framework. The contribution of this paper is two-fold. First, it offers a methodological approach to…
Boolean functions are mathematical objects used in diverse applications. Different applications also have different requirements, making the research on Boolean functions very active. In the last 30 years, evolutionary algorithms have been…
The information processing abilities of a multilayer neural network with a number of hidden units scaling as the input dimension are studied using statistical mechanics methods. The mapping from the input layer to the hidden units is…
A generating function for reciprocal binomial coefficients is written down, integral representations of this function are obtained, generating functions for sums of reciprocal binomial coefficients are derived, new identities are obtained,…
Polynomial threshold gates are basic processing units of an artificial neural network. When the input vectors are binary vectors, these gates correspond to Boolean functions and can be analyzed via their polynomial representations. In…
Grammatic is a tool for grammar definition and manipulation aimed to improve modularity and reuse of grammars and related development artifacts. It is independent from parsing technology and any other details of target system…
We give several different encodings of the step function of a Turing machine in intuitionistic linear logic, and calculate the denotations of these encodings in the Sweedler semantics.
We propose a new multi-agent task grammar to encode collaborative tasks for a team of heterogeneous agents that can have overlapping capabilities. The grammar allows users to specify the relationship between agents and parts of the task…