Related papers: Knuth-Bendix for groups with infinitely many rules
Synchronizing words in classical automata theory provide a mechanism to reset any state of a deterministic automaton to a specific target state via a carefully chosen finite sequence of transition rules. In this work, we extend the concept…
This is Chapter 24 in the "AutoMathA" handbook. Finite automata have been used effectively in recent years to define infinite groups. The two main lines of research have as their most representative objects the class of automatic groups…
We introduce the notion of expandability in the context of automaton semigroups and groups: a word is k-expandable if one can append a suffix to it such that the size of the orbit under the action of the automaton increases by at least k.…
In this work we use a framework of finite-state automata constructions based on equivalences over words to provide new insights on the relation between well-known methods for computing the minimal deterministic automaton of a language.
We describe an active-set method for the minimization of an objective function $\phi$ that is the sum of a smooth convex function and an $\ell_1$-regularization term. A distinctive feature of the method is the way in which active-set…
This paper describes a novel method of compiling ranked tagging rules into a deterministic finite-state device called a bimachine. The rules are formulated in the framework of regular rewrite operations and allow unrestricted regular…
The states of a deterministic finite automaton A can be identified with collections of words in Pf(L(A)) -- the set of prefixes of words belonging to the regular language accepted by A. But words can be ordered and among the many possible…
In automata theory, while determinisation provides a standard route to solving many common problems in automata theory, some weak forms of nondeterminism can be dealt with in some problems without costly determinisation. For example, the…
Compiling quantum circuits lends itself to an elegant formulation in the language of rewriting systems on non commutative polynomial algebras $\mathbb Q\langle X\rangle$. The alphabet $X$ is the set of the allowed hardware 2-qubit gates.…
We show the NP-completeness of the existential theory of term algebras with the Knuth-Bendix order by giving a nondeterministic polynomial-time algorithm for solving Knuth-Bendix ordering constraints.
We introduce a quantum analogue of a classical synchronizing automaton. In classical case the state of a system evolves according to a set of rules forming an alphabet, and sequences of these rules, called words, govern its evolution.…
We consider grammar-restricted exact learning of formulas and terms in finite variable logics. We propose a novel and versatile automata-theoretic technique for solving such problems. We first show results for learning formulas that…
Given an infinite linear group with a finite set of generators, we show that the shortest word length of an element of infinite order has an upper bound that depends only on the number of generators and the degree. This provides a…
We investigate the nondeterministic state complexity of basic operations for suffix-free regular languages. The nondeterministic state complexity of an operation is the number of states that are necessary and sufficient in the worst-case…
Jumping automata are finite automata that read their input in a non-consecutive manner, disregarding the order of the letters in the word. We introduce and study jumping automata over infinite words. Unlike the setting of finite words,…
By limiting the range of the predicate variables in a second-order language one may obtain restricted versions of second-order logic such as weak second-order logic or definable subset logic. In this note we provide an infinitary strongly…
In this paper we introduce a new type of approximate state reductions where the behaviors of the reduced and the original automaton do not have to be identical, but they must match on all words of length less than or equal to some given…
The paper discusses the problem of determinising finite-state automata containing large numbers of epsilon-moves. Experiments with finite-state approximations of natural language grammars often give rise to very large automata with a very…
We introduce an efficient method to reconstruct the Wigner function of many-mode continuous variable systems. It is based on convex optimization with semidefinite programs, and also includes a version of the maximum entropy principle, in…
These notes present the essentials of first- and second-order monadic logics on strings with introductory purposes. We discuss Monadic First-Order logic and show that it is strictly less expressive than Finite-State Automata, in that it…