Related papers: On Shuffling and Splitting Automata

Parametric timed automata (PTAs) are a powerful formalism to reason, simulate and formally verify critical real-time systems. After 25 years of research on PTAs, it is now well-understood that any non-trivial problem studied is undecidable…

We introduce and study input-driven deterministic and nondeterministic double-head pushdown automata. A double-head pushdown automaton is a slight generalization of an ordinary pushdown automaton working with two input heads that move in…

In this article, we study classes of multidimensional subshifts defined by multihead finite automata, in particular the hierarchy of classes of subshifts defined as the number of heads grows. The hierarchy collapses on the third level,…

We study the polyregular string-to-string functions, which are certain functions of polynomial output size that can be described using automata and logic. We describe a system of combinators that generates exactly these functions. Unlike…

We study the splitting of the Goodwillie towers of functors in various settings. In particular, we produce splitting criteria for functors $F: \A \to M_A$ from a pointed category with coproducts to $A$-modules in terms of differentials of…

A featured transition system is a transition system in which the transitions are annotated with feature expressions: Boolean expressions on a finite number of given features. Depending on its feature expression, each individual transition…

We introduce the notion of multipass automata as a generalization of pushdown automata and study the classes of languages accepted by such machines. The class of languages accepted by deterministic multipass automata is exactly the Boolean…

Partially ordered automata are automata where the transition relation induces a partial order on states. The expressive power of partially ordered automata is closely related to the expressivity of fragments of first-order logic on finite…

We extend the classification of mixed states of quantum systems composed of arbitrary number of subsystems of arbitrary dimensions. This extended classification is complete in the sense of partial separability and gives 1+18+1 partial…

The zero divisor conjecture is sufficient to prove for certain class of finitely presented groups where the relations are given by a pairing of generators. We associate Mealy automata to such pairings, and prove that the zero divisor…

We show that a well-known family of deterministic finite automata can be used to distinguish distinct binary strings of the same length from every start state. Further, we establish almost matching lower and upper bounds on the number of…

We consider decision problems for relations over finite and infinite words defined by finite automata. We prove that the equivalence problem for binary deterministic rational relations over infinite words is undecidable in contrast to the…

In formal language theory, several different models characterize regular languages, such as finite automata, congruences of finite index, or monadic second-order logic (MSO). Moreover, several fragments of MSO have effective…

We study an expressive model of timed pushdown automata extended with modular and fractional clock constraints. We show that the binary reachability relation is effectively expressible in hybrid linear arithmetic with a rational and an…

By algorithmic metatheorems for a model checking problem P over infinite-state systems we mean generic results that can be used to infer decidability (possibly complexity) of P not only over a specific class of infinite systems, but over a…

The goal of this paper is to provide exact and terminating algorithms for the formal analysis of deterministic continuous-time control systems with affine input and polynomial state dynamics (in short, polynomial systems). We consider the…

We discuss various formalisms to describe string-to-string transformations. Many are based on automata and can be seen as operational descriptions, allowing direct implementations when the input scanner is deterministic. Alternatively, one…

The notion of non-deterministic logical matrix (where connectives are interpreted as multi-functions) preserves many good properties of traditional semantics based on logical matrices (where connectives are interpreted as functions) whilst…

We answer an open question in the theory of transducer degrees initially posed in [3], on the structure of polynomial transducer degrees, in particular the question of what degrees, if any, lie below the degree of $n^3$. Transducer degrees…

First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…