Related papers: Partial Derivative Automaton for Regular Expressio…
We introduce a new complexity measure for finite strings using probabilistic finite-state automata (PFAs), in the same spirit as existing notions employing DFAs and NFAs, and explore its properties. The PFA complexity $A_P(x)$ is the least…
A \emph{data automaton} is a finite automaton equipped with variables (counters or registers) ranging over infinite data domains. A trace of a data automaton is an alternating sequence of alphabet symbols and values taken by the counters…
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…
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…
Semi-automata are abstractions of electronic devices that are deterministic finite-state machines having inputs but no outputs. Generalized semiautomata are obtained from stochastic semiautomata by dropping the restrictions imposed by…
We study extremal and algorithmic questions of subset and careful synchronization in monotonic automata. We show that several synchronization problems that are hard in general automata can be solved in polynomial time in monotonic automata,…
Partial derivatives are used in a variety of different ways within physics. Most notably, thermodynamics uses partial derivatives in ways that students often find confusing. As part of a collaboration with mathematics faculty, we are at the…
We show that if M is a DFA with n states over an arbitrary alphabet and L = L(M), then the worst-case state complexity of L^2 is n*2^n - 2^{n-1}. If, however, M is a DFA over a unary alphabet, then the worst-case state complexity of L^k is…
The simulation of deterministic pushdown automata defined over a one-letter alphabet by finite state automata is investigated from a descriptional complexity point of view. We show that each unary deterministic pushdown automaton of size s…
The equivalence of finite automata and regular expressions dates back to the seminal paper of Kleene on events in nerve nets and finite automata from 1956. In the present paper we tour a fragment of the literature and summarize results on…
Unambiguous B\"uchi automata, i.e. B\"uchi automata allowing only one accepting run per word, are a useful restriction of B\"uchi automata that is well-suited for probabilistic model-checking. In this paper we propose a more permissive…
The aim of this paper is to design the polynomial construction of a finite recognizer for hairpin completions of regular languages. This is achieved by considering completions as new expression operators and by applying derivation…
Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional…
We consider the 1d Schr\"odinger operator with random decaying potential and compute the 2nd term asymptotics of the density of states, which shows substantial differences between the cases $\alpha > \frac 12$, $\alpha < \frac 12$ and…
In this paper we consider a nondeterministic computation by deterministic multi-head 2-way automata having a read-only access to an auxiliary memory. The memory contains additional data (a guess) and computation is successful iff it is…
We identify a subclass of the regular commutative languages that is closed under the iterated shuffle, or shuffle closure. In particular, it is regularity-preserving on this subclass. This subclass contains the commutative group languages…
We consider random walks on the set of all words over a finite alphabet such that in each step only the last two letters of the current word may be modified and only one letter may be adjoined or deleted. We assume that the transition…
An index for a finite automaton is a powerful data structure that supports locating paths labeled with a query pattern, thus solving pattern matching on the underlying regular language. In this paper, we solve the long-standing problem of…
A Milstein-type scheme was proposed to improve the rate of convergence of its approximation of the solution to a stochastic differential equation driven by a vector of continuous semimartingales. A necessary and sufficient condition was…
We characterize the minimum-length sequences of independent lazy simple transpositions whose composition is a uniformly random permutation. For every reduced word of the reverse permutation there is exactly one valid way to assign…