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We present decidability results for termination of classes of term rewriting systems modulo permutative theories. Termination and innermost termination modulo permutative theories are shown to be decidable for term rewrite systems (TRS)…
A three-way (resp., two-way) two-dimensional automaton has a read-only input head that moves in three (resp., two) directions on a finite array of cells labelled by symbols of the input alphabet. Restricting the input head movement of a…
A channel machine consists of a finite controller together with several fifo channels; the controller can read messages from the head of a channel and write messages to the tail of a channel. In this paper, we focus on channel machines with…
Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…
The theory of computation is based on abstract computing automata which can be classified into a three-class hierarchy: Finite Automata (FA), Push-down Automata (PDA) and the Turing Machines (TM). Each class corresponds to grammar/language…
Let W~ be an affine Weyl group, and let C be a left, right, or two-sided Kazhdan--Lusztig cell in W~. Let Reduced (C) be the set of all reduced expressions of elements of C, regarded as a formal language in the sense of the theory of…
Reversible weighted automata are introduced and considered in a specific setting where the weights are taken from a nontrivial locally finite commutative ring such as a finite field. It is shown that the supports of series realised by such…
We consider finite deterministic automata such that their alphabets consist of exactly one letter of defect 1 and a set of permutations of the state set. We study under which conditions such an automaton is completely reachable. We focus…
Reversibility of a one-dimensional finite cellular automaton (CA) is dependent on lattice size. A finite CA can be reversible for a set of lattice sizes. On the other hand, reversibility of an infinite CA, which is decided by exploring the…
We study structural restrictions on biautomata such as, e.g., acyclicity, permutation-freeness, strongly permutation-freeness, and orderability, to mention a few. We compare the obtained language families with those induced by deterministic…
Watson-Crick (WK) finite automata work on a Watson-Crick tape representing a DNA molecule. They have two reading heads. In 5'->3' WK automata, the heads move and read the input in opposite physical directions. In this paper, we consider…
Text normalization (TN) systems in production are largely rule-based using weighted finite-state transducers (WFST). However, WFST-based systems struggle with ambiguous input when the normalized form is context-dependent. On the other hand,…
We examine inkdots placed on the input string as a way of providing advice to finite automata, and establish the relations between this model and the previously studied models of advised finite automata. The existence of an infinite…
We consider the previously defined notion of finite-state independence and we focus specifically on normal words. We characterize finite-state independence of normal words in three different ways, using three different kinds of asynchronous…
Symbolic automata are finite state automata that support potentially infinite alphabets, such as the set of rational numbers, generally applied to regular expressions/languages over finite words. In symbolic automata (or automata modulo…
We prove that a semigroup generated by a reversible two-state Mealy automaton is either finite or free of rank 2. This fact leads to the decidability of finiteness for groups generated by two-state or two-letter invertible-reversible Mealy…
A deterministic finite-state automaton (FSA) is an abstract sequential machine that reads the symbols comprising an input word one at a time. An FSA is symmetric if its output is independent of the order in which the input symbols are read,…
We introduce a new measure on regular languages: their nondeterministic syntactic complexity. It is the least degree of any extension of the `canonical boolean representation' of the syntactic monoid. Equivalently, it is the least number of…
This paper proposes a new end-to-end text-to-speech (E2E-TTS) model based on neural machine translation (NMT). The proposed model consists of two components; a non-autoregressive vector quantized variational autoencoder (VQ-VAE) model and…
Transformers are ubiquitous models in the natural language processing (NLP) community and have shown impressive empirical successes in the past few years. However, little is understood about how they reason and the limits of their…