Related papers: On minimising automata with errors
The fuzzy $K$-means problem is a generalization of the classical $K$-means problem to soft clusterings, i.e. clusterings where each points belongs to each cluster to some degree. Although popular in practice, prior to this work the fuzzy…
Several new algorithms for deciding emptiness of Boolean combinations of regular languages and of languages of alternating automata (AFA) have been proposed recently, especially in the context of analysing regular expressions and in string…
A central question in the theory of automata is which classes of automata can be minimized in polynomial time. We close the remaining gaps for deterministic and history-deterministic automata over infinite words by proving that…
The problem of inclusion of the language accepted by timed automaton $A$ (e.g., the implementation) in the language accepted by $B$ (e.g., the specification) is, in general, undecidable in the class of non-deterministic timed automata. In…
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 investigate means of efficient computation of the simulation relation over symbolic finite automata (SFAs), i.e., finite automata with transitions labeled by predicates over alphabet symbols. In one approach, we build on the algorithm by…
This article gives theoretical insights into the performance of K-SVD, a dictionary learning algorithm that has gained significant popularity in practical applications. The particular question studied here is when a dictionary $\Phi\in…
Automata learning has many applications in artificial intelligence and software engineering. Central to these applications is the $L^*$ algorithm, introduced by Angluin. The $L^*$ algorithm learns deterministic finite-state automata (DFAs)…
The class of local languages is a well-known subclass of the regular languages that admits many equivalent characterizations. In this short note we establish the PSPACE-completeness of the problem of determining, given as input a…
Angluin's L$^*$ algorithm learns the minimal deterministic finite automaton (DFA) of a regular language using membership and equivalence queries. Its probabilistic approximatively correct (PAC) version substitutes an equivalence query by…
We study several problems related to finding reset words in deterministic finite automata. In particular, we establish that the problem of deciding whether a shortest reset word has length k is complete for the complexity class DP. This…
Neural networks offer good approximation to many tasks but consistently fail to reach perfect generalization, even when theoretical work shows that such perfect solutions can be expressed by certain architectures. Using the task of formal…
We present an algorithm for regular expression parsing and submatch extraction based on tagged deterministic finite automata. The algorithm works with different disambiguation policies. We give detailed pseudocode for the algorithm,…
Recently, min-max optimization problems have received increasing attention due to their wide range of applications in machine learning (ML). However, most existing min-max solution techniques are either single-machine or distributed…
In this paper, we introduce the problem of rewriting finite formal languages using syntactic macros such that the rewriting is minimal in size. We present polynomial-time algorithms to solve variants of this problem and show their…
We consider a standard distributed optimisation setting where $N$ machines, each holding a $d$-dimensional function $f_i$, aim to jointly minimise the sum of the functions $\sum_{i = 1}^N f_i (x)$. This problem arises naturally in…
The paper completely characterizes the primality of acyclic DFAs, where a DFA $\mathcal{A}$ is prime if there do not exist DFAs $\mathcal{A}_1,\dots,\mathcal{A}_t$ with $\mathcal{L}(\mathcal{A}) = \bigcap_{i=1}^{t}…
A discounted-sum automaton (NDA) is a nondeterministic finite automaton with edge weights, valuing a run by the discounted sum of visited edge weights. More precisely, the weight in the i-th position of the run is divided by $\lambda^i$,…
The k-means algorithm is one of the most common clustering algorithms and widely used in data mining and pattern recognition. The increasing computational requirement of big data applications makes hardware acceleration for the k-means…
Designing short DNA words is a problem of constructing a set (i.e., code) of n DNA strings (i.e., words) with the minimum length such that the Hamming distance between each pair of words is at least k and the n words satisfy a set of…