Related papers: Language of Boolean functions its Grammar and Mach…
This paper presents a scalable method for integrating compositional morphological representations into a vector-based probabilistic language model. Our approach is evaluated in the context of log-bilinear language models, rendered suitably…
We introduce a high-level language with Python-like syntax for string-to-string, polyregular, first-order definable transductions. This language features function calls, boolean variables, and nested for-loops. We devise and implement a…
An algorithm is designed which decomposes a tropical univariate rational function into a composition of tropical binomials and trinomials. When a function is monotone, the composition consists just of binomials. Similar algorithms are…
In this paper, we focus on the links between Boolean function theory and quantum computing. In particular, we study the notion of what we call fully-balanced functions and analyse the Fourier--Hadamard and Walsh supports of those functions…
Subword tokenization has become the de-facto standard for tokenization, although comparative evaluations of subword vocabulary quality across languages are scarce. Existing evaluation studies focus on the effect of a tokenization algorithm…
In the principles-and-parameters framework, the structural features of languages depend on parameters that may be toggled on or off, with a single parameter often dictating the status of multiple features. The implied covariance between…
A novel polynomial expansion method of symmetric Boolean functions is described. The method is efficient for symmetric Boolean function with small set of valued numbers and has the linear complexity for elementary symmetric Boolean…
The paper discusses the problem of determinising finite-state automata containing large numbers of epsilon-moves. Experiments with finite-state approximations of natural language grammars often give rise to very large automata with a very…
We investigate the influences of variables on a Boolean function $f$ based on the quantum Bernstein-Vazirani algorithm. A previous paper (Floess et al. in Math. Struct. in Comp. Science 23: 386, 2013) has proved that if a $n$-variable…
Bernstein-Vazirani algorithm (the one-query algorithm) can identify a completely specified linear Boolean function using a single query to the oracle with certainty. The first aim of the paper is to show that if the provided Boolean…
Algorithms are the engine for reproducible problem-solving. We present a framework automating algorithm discovery by conceptualizing them as sequences of operations, represented as tokens. These computational tokens are chained using a…
Obtained a new property of superposition of the generating functions ln(1/(1-F(x))), where F(x) - generating function with integer coefficients, which allows the construction a primality tests. The theorem which is based on compositions of…
The concepts of amenable and compatible functions have been introduced in a recent work, in order to state precise mathematical theorems that guarantee that a backward stable algorithm is also forward stable, and that the composition of two…
We define an algorithm to be the set of programs that implement or express that algorithm. The set of all programs is partitioned into equivalence classes. Two programs are equivalent if they are essentially the same program. The set of…
In this paper we discuss an efficient technique that can implement any given Boolean function as a quantum circuit. The method converts a truth table of a Boolean function to the corresponding quantum circuit using a minimal number of…
We compute the motivic nearby cycles of functions obtained by composition of two functions with distinct sets of variables with a two variable function
The mechanisms of comprehension during language processing remains an open question. Classically, building the meaning of a linguistic utterance is said to be incremental, step-by-step, based on a compositional process. However, many…
Large Language Models (LLMs) have exhibited significant potential in performing diverse tasks, including the ability to call functions or use external tools to enhance their performance. While current research on function calling by LLMs…
We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these…
A reinforcement learning algorithm accomplishes the task of synthesizing a set-theoretical formula that evaluates to given truth values for given assignments.