Consider an extension of the classical model of finite automata operating on finite strings in which the machine simultaneously reads a fixed advice tape — an infinite string A. A deterministic finite-string automaton with advice A is like a deterministic finite-string automaton, except that at step n the next state depends on the current state, the nth symbol of the input w ∈ Σ∗, and the nth s...

We generalize the classical Myhill-Nerode theorem for finite automata to the setting of sequential transducers over unique GCDmonoids, which are cancellative monoids in which every two non-zero elements admit a unique greatest common (left) divisor. We prove that a given formal power series is sequential, if and only if it is directed and our Myhill-Nerode equivalence relation has finite index....

In order to model concurrency, we extend automata theory from the usual word languages (sets of labelled linear orders) to sets of labelled series-parallel posets | or, equivalently, to sets of terms in an algebra with two product operations: sequential and parallel. We rst consider languages of posets having bounded width, and characterize them using depth-nilpotent algebras. Next we introduce...

In this paper we consider when a linear functional on a bialgebra is realized by the action of the bialgebra on a finite object. This depends on whether the action of the bialgebra on the functional is finite. We consider two specific cases: the Myhill–Nerode Theorem, which gives a condition for a language to be accepted by a finite automaton, and Fliess’ Theorem, which gives a condition for fo...

Order-Preserving DAG Grammars (OPDGs) is a subclass of Hyper-Edge Replacement Grammars that can be parsed in polynomial time. Their associated class of languages is known as Ordered DAG Languages, and the graphs they generate are characterised by being acyclic, rooted, and having a natural order on their nodes. OPDGs are useful in natural-language processing to model abstract meaning representa...

We present a learning algorithm for regular languages that unifies three existing ones for the settings of minimally adequate teacher learning, learning from membership queries and positive data, and learning from positive and negative data, respectively. We choose these three algorithms as an example to back up the conjecture that the learning process of every algorithm for the class of regula...

We formally verify translations from two-way automata to one-way automata based on results from the literature. Following Vardi, we obtain a simple reduction from nondeterministic two-way automata to one-way automata that leads to a doubly-exponential increase in the number of states. By adapting the work of Shepherdson and Vardi, we obtain a singlyexponential translation from nondeterministic ...

The purpose of this work is to introduce and study the concept of minimal deterministic automaton with IF-outputs which realizes the given IF-language. Among two methods for construction of such automaton presented here, one is based on Myhill-Nerode’s theory while the other is based on derivatives of the given IF-language. Meanwhile, the categories of deterministic automata with IF-outputs and...

We study the problem of learning sequential top-down tree-toword transducers (stws). First, we present a Myhill-Nerode characterization of the corresponding class of sequential tree-to-word transformations (ST W). Next, we investigate what learning of stws means, identify fundamental obstacles, and propose a learning model with abstain. Finally, we present a polynomial learning algorithm.

Set constraints are inclusions between expressions denoting sets of ground terms over a finite ranked alphabet Σ. Rational spaces are topological spaces obtained as spaces of runs of topological Σhypergraphs. They were introduced by Kozen in [Koz95], where the topological structure of the spaces of solutions to systems of set constraints was given in terms of rational spaces. In this paper we c...