Related papers: On (co-lex) Ordering Automata
This paper examines several measures of space complexity of variants of stack automata: non-erasing stack automata and checking stack automata. These measures capture the minimum stack size required to accept every word in the language of…
Compact representations of automata are important for efficiency. In this paper, we study methods to compute reduced automata, in which no two states accept the same language. We do this for finitary automata (FA), an abstract definition…
The automatic complexity of a finite word (string) is an analogue for finite automata of Sipser's distinguishing complexity (1983) and was introduced by Shallit and Wang (2001). For a finite alphabet $\Sigma$ of at least two elements, we…
Saturation is a fundamental game-semantic property satisfied by strategies that interpret higher-order concurrent programs. It states that the strategy must be closed under certain rearrangements of moves, and corresponds to the intuition…
Hyperproperties lift conventional trace properties from a set of execution traces to a set of sets of execution traces. Hyperproperties have been shown to be a powerful formalism for expressing and reasoning about information-flow security…
We consider two natural problems about nondeterministic finite automata. First, given such an automaton M of n states, and a length l, does M accept a word of length l? We show that the classic problem of triangle-free graph recognition…
A goal of this paper is to introduce the new construction of an automaton with shortest synchronizing word of length $O(d^{\frac{n}{d}})$, where $d \in \mathbb{N}$ and $n$ is the number of states for that automaton. Additionally we…
In this paper we explore languages of higher-dimensional automata (HDAs) from an algebraic and logical point of view. Such languages are sets of finite width-bounded interval pomsets with interfaces (ipomsets) closed under order extension.…
We characterize complete deterministic finite automata with two input letters in which every non-empty set of states occurs as the image of the whole state set under the action of a suitable input word. The characterization leads to a…
Most slowly synchronizing automata over binary alphabets are circular, i.e., containing a letter permuting the states in a single cycle, and their set of synchronizing words has maximal state complexity, which also implies complete…
We define a new subclass of nondeterministic finite automata for prefix-closed languages called Flanked Finite Automata (FFA). We show that this class enjoys good complexity properties while preserving the succinctness of nondeterministic…
Given a right-infinite word $\bf x$ over a finite alphabet $A$, the rank of $\bf x$ is the size of the smallest set $S$ of words over $A$ such that $\bf x$ can be realized as an infinite concatenation of words in $S$. We show that the…
The theory of higher-dimensional automata (HDAs) has seen rapid progress in recent years, and first applications, notably to Petri net analysis, are starting to show. It has, however, emerged that HDAs themselves often are too strict a…
For some fixed alphabet A, a language L of A* is in the class L(1/2) of the Straubing-Therien hierarchy if and only if it can be expressed as a finite union of languages A*aA*bA*...A*cA*, where a,b,...,c are letters. The class L(1) is…
In this paper, we introduce rerailing automata for $\omega$-regular languages. They generalize both deterministic parity (DPW) and minimized history-deterministic co-B\"uchi automata (with transition based acceptance, HdTbcBW) while…
Partially ordered nondeterminsitic finite automata (poNFAs) are NFAs whose transition relation induces a partial order on states, that is, for which cycles occur only in the form of self-loops on a single state. A poNFA is universal if it…
A characteristic sample for a language $L$ and a learning algorithm $\textbf{L}$ is a finite sample of words $T_L$ labeled by their membership in $L$ such that for any sample $T \supseteq T_L$ consistent with $L$, on input $T$ the learning…
We introduce partially ordered two-way B\"uchi automata and characterize their expressive power in terms of fragments of first-order logic FO[<]. Partially ordered two-way B\"uchi automata are B\"uchi automata which can change the direction…
The article continues the study of the genus of regular languages that the authors introduced in a 2012 paper. Generalizing a previous result, we produce a new family of regular languages on a two-letter alphabet having arbitrary high…
A $d$-limited automaton is a Turing machine that may rewrite each input cell at most~$d$ times. Hibbard (1967) showed that for every $d \geq 2$ such automata recognize all context-free languages and that deterministic $d$-limited automata…