Search results for " Automata theory"
showing 10 items of 266 documents
Integer Weighted Regression Tsetlin Machines
2020
The Regression Tsetlin Machine (RTM) addresses the lack of interpretability impeding state-of-the-art nonlinear regression models. It does this by using conjunctive clauses in propositional logic to capture the underlying non-linear frequent patterns in the data. These, in turn, are combined into a continuous output through summation, akin to a linear regression function, however, with non-linear components and binary weights. However, the resolution of the RTM output is proportional to the number of clauses employed. This means that computation cost increases with resolution. To address this problem, we here introduce integer weighted RTM clauses. Our integer weighted clause is a compact r…
A Musical Pattern Discovery System Founded on a Modeling of Listening Strategies
2004
Music is a domain of expression that conveys a paramount degree of complexity. The musical surface, composed of a multitude of notes, results from the elaboration of numerous structures of different types and sizes. The composer constructs this structural complexity in a more or less explicit way. The listener, faced by such a complex phenomenon, is able to reconstruct only a limited part of it, mostly in a non-explicit way. One particular aim of music analysis is to objectify such complexity, thus offering to the listener a tool for enriching the appreciation of music (Lartillot and SaintJames, 2004). The trouble is, traditional musical analysis, although offering a valuable understanding …
FO^2 with one transitive relation is decidable
2013
We show that the satisfiability problem for the two-variable first-order logic, FO^2, over transitive structures when only one relation is required to be transitive, is decidable. The result is optimal, as FO^2 over structures with two transitive relations, or with one transitive and one equivalence relation, are known to be undecidable, so in fact, our result completes the classification of FO^2-logics over transitive structures with respect to decidability. We show that the satisfiability problem is in 2-NExpTime. Decidability of the finite satisfiability problem remains open.
Unambiguous recognizable two-dimensional languages
2006
We consider the family UREC of unambiguous recognizable two-dimensional languages. We prove that there are recognizable languages that are inherently ambiguous, that is UREC family is a proper subclass of REC family. The result is obtained by showing a necessary condition for unambiguous recognizable languages. Further UREC family coincides with the class of picture languages defined by unambiguous 2OTA and it strictly contains its deterministic counterpart. Some closure and non-closure properties of UREC are presented. Finally we show that it is undecidable whether a given tiling system is unambiguous.
Weak and strong recognition by 2-way randomized automata
1997
Languages weakly recognized by a Monte Carlo 2-way finite automaton with n states are proved to be strongly recognized by a Monte Carlo 2-way finite automaton with no(n) states. This improves dramatically over the previously known result by M.Karpinski and R.Verbeek [10] which is also nontrivial since these languages can be nonregular [5]. For tally languages the increase in the number of states is proved to be only polynomial, and these languages are regular.
Block-Deterministic Regular Languages
2001
We introduce the notions of blocked, block-marked and blockdeterministic regular expressions. We characterize block-deterministic regular expressions with deterministic Glushkov block automata. The results can be viewed as a generalization of the characterization of one-unambiguous regular expressions with deterministic Glushkov automata. In addition, when a language L has a block-deterministic expression E, we can construct a deterministic finite-state automaton for L that has size linear in the size of E.
Epichristoffel Words and Minimization of Moore Automata
2014
This paper is focused on the connection between the combinatorics of words and minimization of automata. The three main ingredients are the epichristoffel words, Moore automata and a variant of Hopcroft's algorithm for their minimization. Epichristoffel words defined in [14] generalize some properties of circular sturmian words. Here we prove a factorization property and the existence of the reduction tree, that uniquely identifies the structure of the word. Furthermore, in the paper we investigate the problem of the minimization of Moore automata by defining a variant of Hopcroft's minimization algorithm. The use of this variant makes simpler the computation of the running time and consequ…
A note on renewal systems
1992
Abstract A renewal system is a symbolic dynamical system generated by free concatenations of a finite set of words. In this paper we prove that, given two systems which are both renewal and Markov systems, it is decidable whether they are topologically conjugate. The proof makes use of the methods and the techniques of formal language theory.
On Sturmian Graphs
2007
AbstractIn this paper we define Sturmian graphs and we prove that all of them have a certain “counting” property. We show deep connections between this counting property and two conjectures, by Moser and by Zaremba, on the continued fraction expansion of real numbers. These graphs turn out to be the underlying graphs of compact directed acyclic word graphs of central Sturmian words. In order to prove this result, we give a characterization of the maximal repeats of central Sturmian words. We show also that, in analogy with the case of Sturmian words, these graphs converge to infinite ones.
A decidable word problem without equivalent canonical term rewriting system
1989
We present a weak associative single-axiom system having the following property: the word problem is decidable with an efficient algorithm even though there does not exist any finite equivalent canonical term rewriting system.