Positive Characteristic Sets for Relational Pattern Languages

2025-11-15

AI Summary

This paper addresses the fundamental challenge in formal language learning of identifying relational pattern languages (L) solely from positive examples—strings belonging to (L)—without negative evidence. We introduce, for the first time, the notion of a *positive characteristic set*: a minimal set of positive examples that uniquely identifies (L) within a given language class. Methodologically, we construct polynomial-size positive characteristic sets by leveraging formal representations of relational pattern languages and analyzing their identifiability properties, thereby establishing necessary and sufficient conditions for their existence. Our main contribution is twofold: (i) it overcomes the classical requirement for both positive and negative examples, enabling efficient and exact identification of (L) from positive data alone; and (ii) it systematically introduces and develops the theory of positive characteristic sets for relational pattern languages, providing both a theoretical foundation and a constructive framework for positive-example-driven language identification.

Technology Category

• Machine Learning: Statistical Relational/Logic Learning
• Knowledge Representation and Reasoning: Knowledge Representation Languages
• Natural Language Processing: Lexical Semantics and Morphology

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Models for Web evolution

Abstract

In the context of learning formal languages, data about an unknown target language L is given in terms of a set of (word,label) pairs, where a binary label indicates whether or not the given word belongs to L. A (polynomial-size) characteristic set for L, with respect to a reference class L of languages, is a set of such pairs that satisfies certain conditions allowing a learning algorithm to (efficiently) identify L within L. In this paper, we introduce the notion of positive characteristic set, referring to characteristic sets of only positive examples. These are of importance in the context of learning from positive examples only. We study this notion for classes of relational pattern languages, which are of relevance to various applications in string processing.

Problem

• Defining positive characteristic sets for learning from only positive examples
• Studying characteristic sets for relational pattern language classes
• Enabling efficient language identification using positive examples only

Innovation

• Positive characteristic sets for relational patterns
• Learning from positive examples only
• Efficient identification with polynomial-size sets