Mathematics of Language 

About: Mathematics of Language is an academic conference. The conference publishes majorly in the area(s): Context-sensitive grammar & Tree-adjoining grammar. Over the lifetime, 114 publications have been published by the conference receiving 1086 citations.

On languages piecewise testable in the strict sense

Abstract: In this paper we explore the class of Strictly Piecewise languages, originally introduced to characterize long-distance phonotactic patterns by Heinz [7] as the Precedence Languages. We provide a series of equivalent abstract characterizations, discuss their basic properties, locate them relative to other well-known subregular classes and provide algorithms for translating between the grammars defined here and finite state automata as well as an algorithm for deciding whether a regular language is Strictly Piecewise.

Analogy and Formal Languages

Abstract: In this paper, we advocate a study of analogies between strings of symbols for their own sake. We show how some sets of strings, i.e., some formal languages, may be characterized by use of analogies. We argue that some preliminary “good properties” obtained may plead in favour of the use of analogy in the study of formal languages in relationship with natural language.

Vowel Harmony and Subsequentiality

Abstract: Attested and ‘pathological’ vowel harmony patterns are studied in the context of subclasses of regular functions. The analysis suggests that the computational complexity of phonology can be reduced from regular to weakly deterministic.

A Concatenation Operation to Derive Autosegmental Graphs

Abstract: Autosegmental phonology represents words with graph structures. This paper introduces a way of reasoning about autosegmental graphs as strings of concatenated graph primitives. The main result shows that the sets of autosegmental graphs so generated obey two important, putatively universal, constraints in phonological theory provided that the graph primitives also obey these constraints. These constraints are the Obligatory Contour Principle and the No Crossing Constraint. Thus, these constraints can be understood as being derived from a finite basis under concatenation. This contrasts with (and complements) earlier analyses of autosegmental representations, where these constraints were presented as axioms of the grammatical system. Empirically motivated examples are provided.

On the Logical Complexity of Autosegmental Representations

Abstract: Autosegmental mapping from disjoint strings of tones and tone-bearing units, a commonly used mechanism in phonological analyses of tone patterns, is shown to not be definable in monadic second-order logic. This is abnormally complex in comparison to other phonological mappings, which have been shown to be monadic second-order definable. In contrast, generation of autosegmental structures from strings is demonstrated to be first-order definable.