It has been argued that rule-based phonological descriptions can uniformly be expressed as mappings carried out by finite-state transducers, and therefore fall within the class of rational relations. If this property of generative capacity is an empirically correct characterization of phonological mappings, it should hold of any sufficiently restrictive theory of phonology, whether it utilizes ...

If φ is a scattered order type, μ a cardinal, then there exists a scattered order type ψ such that ψ → [φ] μ,א0 holds. In this note we prove a Ramsey type statement on scattered order types. A trivial fact on ordinals implies the following statement. If μ is an infinite cardinal, then μ → (μ+)1μ. It is less trivial but still easy to show that if φ is an order type, μ a cardinal then there is so...

A rational agent adopts (or changes) its goals when new information (beliefs) becomes available or its desires (e.g., tasks it is supposed to carry out) change. In conventional approaches to goal generation in which a goal is considered as a “particular” desire, a goal is adopted if and only if all conditions leading to its generation are satisfied. It is then supposed that all beliefs are equa...

We study an instance of the inclusion problem for rational relations over words. In this paper we show how to check if a one generator submonoid {w}∗ ⊆ (Σ∗) is included in the prefix closure of a rational relation R ⊆ (Σ∗) given by a multi-tape finite automaton.

We introduce rational semimodules over semirings whose addition is idempotent, like the max-plus semiring, in order to extend the geometric approach of linear control to discrete event systems. We say that a subsemimodule of the free semimodule Sn over a semiring S is rational if it has a generating family that is a rational subset of Sn, Sn being thought of as a monoid under the entrywise prod...

In [4] Berstel and Sakarovitch pointed out that from a proof given in [2] one can deduce that a rational set of a group G which is included in a subgroup H of G is already rational in H (an explicit proof is given in [12]). They called this “a kind of Fatou property of groups” according to similar properties of certain formal power series [14]. Another kind of Fatou property was shown by Eilenb...

A weighted finite-state machine with n tapes (n-WFSM) defines a rational relation on n strings. The paper recalls important operations on these relations, and an algorithm for their auto-intersection. Through a series of practical applications, it investigates the augmented descriptive power of n-WFSMs, w.r.t. classical 1and 2-WFSMs (acceptors and transducers). Some applications are not feasibl...

The centralizer of a set of words X is the largest set of words C(X) commuting with X: XC(X) = C(X)X. It has been a long standing open question due to Conway, 1971, whether the centralizer of any rational set is rational. While the answer turned out to be negative in general, see Kunc 2004, we prove here that the situation is different for codes: the centralizer of any rational code is rational...

We use language theory to study the rational subset problem for groups and monoids. We show that the decidability of this problem is preserved under graph of groups constructions with finite edge groups. In particular, it passes through free products amalgamated over finite subgroups and HNN extensions with finite associated subgroups. We provide a simple proof of a result of Grunschlag showing...

Set P 0(f, c) = P (f, c). The set P (f) = P 0(f) is the postcritical set of f . We will also use the notion postcritical set for P k(f) for some suitable k ≥ 0. Denote by J(f) the Julia set of f and F (f) the Fatou set of f . Recall that the ω-limit set ω(x) of a point x is the set of all limit points of ∪n≥0f n(x). A periodic point x with period p is a sink if there is a neighborhood around x ...