Related papers: On polynomial grammars extended with substitution
Reasoning about array data structures is a key requirement for many applications in hardware and software verification, especially in combination with machine integers. The Satisfiability Modulo Theories (SMT) theory of extensional arrays…
In the present paper the unconditional convergence and the invertibility of multipliers is investigated. Multipliers are operators created by (frame-like) analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or…
This paper presents a new refutation procedure for multimodular systems of integer constraints that commonly arise when verifying cryptographic protocols. These systems, involving polynomial equalities and disequalities modulo different…
The grammar representation of a narrowing tree for a syntactically deterministic conditional term rewriting system and a pair of terms is a regular tree grammar that generates expressions for substitutions obtained by all possible…
We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation…
This paper addresses the online exact string matching problem which consists in finding all occurrences of a given pattern p in a text t. It is an extensively studied problem in computer science, mainly due to its direct applications to…
We present techniques to prove termination of cycle rewriting, that is, string rewriting on cycles, which are strings in which the start and end are connected. Our main technique is to transform cycle rewriting into string rewriting and…
In this paper, we address the problems of Arabic Text Classification and stemming using Transducers and Rational Kernels. We introduce a new stemming technique based on the use of Arabic patterns (Pattern Based Stemmer). Patterns are…
Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. Indeed, the model-checking problem for…
Learning word embeddings using distributional information is a task that has been studied by many researchers, and a lot of studies are reported in the literature. On the contrary, less studies were done for the case of multiple languages.…
We over-approximate reachability sets in string rewriting by languages defined by admissible factors, called tiles. A sparse set of tiles contains only those that are reachable in derivations, and is constructed by completing an automaton.…
Transformer-based models have achieved state-of-the-art performance on speech translation tasks. However, the model architecture is not efficient enough for streaming scenarios since self-attention is computed over an entire input sequence…
In this paper, the result of applying iterative univariate resultant constructions to multivariate polynomials is analyzed. We consider the input polynomials as generic polynomials of a given degree and exhibit explicit decompositions into…
Session types statically describe communication protocols between concurrent message-passing processes. Unfortunately, parametric polymorphism even in its restricted prenex form is not fully understood in the context of session types. In…
Neural encoder-decoder models have been successful in natural language generation tasks. However, real applications of abstractive summarization must consider additional constraint that a generated summary should not exceed a desired…
Let $S$ be a rational fraction and let $f$ be a polynomial over a finite field. Consider the transform $T(f)=\operatorname{numerator}(f(S))$. In certain cases, the polynomials $f$, $T(f)$, $T(T(f))\dots$ are all irreducible. For instance,…
Any two-way finite state automaton is equivalent to some one-way finite state automaton. This well-known result, shown by Rabin and Scott and independently by Shepherdson, states that two-way finite state automata (even non-deterministic)…
We consider multivariable polynomials over a fixed number field, linear in some of the variables. For a system of such polynomials satisfying certain technical conditions we prove the existence of search bounds for simultaneous zeros with…
A general class of polynomial remainder codes is considered. Such codes are very flexible in rate and length and include Reed-Solomon codes as a special case. As an extension of previous work, two joint error-and-erasure decoding approaches…
We study the problem of indexing irreducible polynomials over finite fields, and give the first efficient algorithm for this problem. Specifically, we show the existence of poly(n, log q)-size circuits that compute a bijection between {1,…