Related papers: A* shortest string decoding for non-idempotent sem…
We present the first deterministic nearly-linear time algorithm for single-source shortest paths with negative edge weights on directed graphs: given a directed graph $G$ with $n$ vertices, $m$ edges whose weights are integer in…
The verification problem for neural networks is verifying whether a neural network will suffer from adversarial samples, or approximating the maximal allowed scale of adversarial perturbation that can be endured. While most prior work…
A pseudo-deterministic algorithm is a (randomized) algorithm which, when run multiple times on the same input, with high probability outputs the same result on all executions. Classic streaming algorithms, such as those for finding heavy…
Given a public transportation network, which and how many passenger routes can potentially be shortest paths, when all possible timetables are taken into account? This question leads to shortest path problems on graphs with interval costs…
We use a semigroup-theoretic construction by Peter Higgins in order to produce, for each even $n$, an $n$-state and 3-letter synchronizing automaton with the following two features: 1) all its input letters act as idempotent selfmaps of…
We consider the problem of walking in an unknown street, for a robot that has a minimal sensing capability. The robot is equipped with a sensor that only detects the discontinuities in depth information (gaps) and can locate the target…
The minimal deterministic finite automaton is generally used to determine regular languages equality. Antimirov and Mosses proposed a rewrite system for deciding regular expressions equivalence of which Almeida et al. presented an improved…
Finite automata (FA) are a fundamental computational abstraction that is widely used in practice for various tasks in computer science, linguistics, biology, electrical engineering, and artificial intelligence. Given an input word, an FA…
We show that every regular language defines a unique nondeterministic finite automaton (NFA), which we call "\'atomaton", whose states are the "atoms" of the language, that is, non-empty intersections of complemented or uncomplemented left…
We propose novel algorithms for sequence prediction based on ideas from stringology. These algorithms are time and space efficient and satisfy mistake bounds related to particular stringological complexity measures of the sequence. In this…
Algorithms which learn environments represented by automata in the past have had complexity scaling with the number of states in the automaton, which can be exponentially large even for automata recognizing regular expressions with a small…
Path planning is typically considered in Artificial Intelligence as a graph searching problem and R* is state-of-the-art algorithm tailored to solve it. The algorithm decomposes given path finding task into the series of subtasks each of…
Many natural language processing systems operate over tokenizations of text to address the open-vocabulary problem. In this paper, we give and analyze an algorithm for the efficient construction of deterministic finite automata (DFA)…
We present novel semiring semantics for abstract reduction systems (ARSs). More precisely, we provide a weighted version of ARSs, where the reduction steps induce weights from a semiring. Inspired by provenance analysis in database theory…
We construct a probabilistic finite automaton (PFA) with 7 states and an input alphabet of 5 symbols for which the PFA Emptiness Problem is undecidable. The only input for the decision problem is the starting distribution. For the proof, we…
We prove that a random automaton with $n$ states and any fixed non-singleton alphabet is synchronizing with high probability (modulo an unpublished result about unique highest trees of random graphs). Moreover, we also prove that the…
The determinisation problem for min-plus (tropical) weighted automata was recently shown to be decidable. However, the proof is purely existential, relying on several non-constructive arguments. Our contribution in this work is twofold:…
In the literature, there exist several interesting hybrid models of finite automata which have both quantum and classical states. We call them semi-quantum automata. In this paper, we compare the descriptional power of these models with…
We look into the problems of comparing nondeterministic discounted-sum automata on finite and infinite words. That is, the problems of checking for automata $A$ and $B$ whether or not it holds that for all words $w$, $A(w)=B(w), A(w) \leq…
Consider a random regular graph with degree $d$ and of size $n$. Assign to each edge an i.i.d. exponential random variable with mean one. In this paper we establish a precise asymptotic expression for the maximum number of edges on the…