Related papers: Register automata with linear arithmetic
We study the computational power of real-time finite automata that have been augmented with a vector of dimension k, and programmed to multiply this vector at each step by an appropriately selected $k \times k$ matrix. Only one entry of the…
Affine automata provide a finite-state computational model that preserves the linear-algebraic structure of quantum computation while operating entirely over the reals. Recent work has shown that affine automata can far surpass classical…
Data trees serve as an abstraction of structured data, such as XML documents. A number of specification formalisms for languages of data trees have been developed, many of them adhering to the paradigm of register automata, which is based…
We propose a query learning algorithm for residual symbolic finite automata (RSFAs). Symbolic finite automata (SFAs) are finite automata whose transitions are labeled by predicates over a Boolean algebra, in which a big collection of…
The theory of finite automata concerns itself with words in a free monoid together with concatenation and without further structure. There are, however, important applications which use alphabets which are structured in some sense. We…
In this Ansatz we consider theoretical constructions of RNA polymers into automata, a form of computational structure. The basis for transitions in our automata are plausible RNA enzymes that may perform ligation or cleavage. Limited to…
Probabilistic timed automata (PTAs) are timed automata (TAs) extended with discrete probability distributions.They serve as a mathematical model for a wide range of applications that involve both stochastic and timed behaviours. In this…
Let $\alpha $ be a $p \times q$ interval matrix with $p \geq q$ and with the endpoints of all its entries in the set of the rational numbers. We prove that, if $\alpha $ contains a rank-$r$ real matrix with $r \in \{2, q-2,q-1,q\}$, then it…
We introduce a logic to express structural properties of automata with string inputs and, possibly, outputs in some monoid. In this logic, the set of predicates talking about the output values is parametric, and we provide sufficient…
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 define guarded variable automata (GVAs), a simple extension of finite automata over infinite alphabets. In this model the transitions are labelled by letters or variables ranging over an infinite alphabet and guarded by conjunction of…
The goal of the present paper is to provide a systematic and comprehensive study of rational stochastic languages over a semiring K \in {Q, Q +, R, R+}. A rational stochastic language is a probability distribution over a free monoid…
Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…
We prove decidability of univariate real algebra extended with predicates for rational and integer powers, i.e., $(x^n \in \mathbb{Q})$ and $(x^n \in \mathbb{Z})$. Our decision procedure combines computation over real algebraic cells with…
A rationally dynamically algebraic (RDA) power series is one that arises as (a component of) the solution of a system of differential equations of the form $\boldsymbol{y}' = F(\boldsymbol{y})$, where $F$ is a vector of rational functions…
We introduce the class of P-finite automata. These are a generalisation of weighted automata, in which the weights of transitions can depend polynomially on the length of the input word. P-finite automata can also be viewed as simple…
Recently, the use of mathematical methods and computer science applications have got significant response among biochemists and biologists to modeling the biological systems. The computational and mathematical methods have enormous…
Cost register automata (CRA) and its subclass, copyless CRA, were recently proposed by Alur et al. as a new model for computing functions over strings. We study some structural properties, expressiveness, and closure properties of copyless…
Test-time compute is central to large reasoning models, yet analysing their reasoning behaviour through generated text is increasingly impractical and unreliable. Response length is often used as a brute proxy for reasoning effort, but this…
This paper connects the classes of weighted alternating finite automata (WAFA), weighted finite tree automata (WFTA), and polynomial automata (PA). First, we investigate the use of trees in the run semantics for weighted alternating…