Practical Aspects of Membership Problem of Watson-Crick Context-free Grammars

TL;DR

This paper compares the WK-CYK algorithm and a new heuristic-based state space search for determining membership in Watson-Crick context-free languages, demonstrating the latter's superior efficiency on longer inputs.

Contribution

It introduces a heuristic-based state space search algorithm for Watson-Crick language membership testing, improving practical efficiency over existing methods.

Findings

State space search outperforms WK-CYK on long inputs (hundreds to thousands of symbols).

Heuristics effectively prune the search space, enabling analysis of longer sequences.

The new algorithm is promising for practical DNA-inspired language processing.

Abstract

This paper focuses on Watson-Crick languages inspired by DNA computing, their models, and algorithms for deciding the language membership. It analyzes a recently introduced algorithm called WK-CYK and introduces a state space search algorithm that is based on regular Breadth-first search but uses a number of optimizations and heuristics to be efficient in practical use and able to analyze longer inputs. The key parts are the heuristics for pruning the state space (detecting dead ends) and heuristics for choosing the most promising branches to continue the search. These two algorithms have been tested with 20 different Watson-Crick grammars (40 including their Chomsky normal form versions). While WK-CYK is able to decide the language membership in a reasonable time for inputs of the length of roughly 30-50 symbols and its performance is very consistent for all kinds of grammars and inputs, the state space search is usually (89-98 % of cases) more efficient and able to do the computation for inputs with lengths of hundreds or even thousands of symbols. Thus, the state space search has the potential to be a good tool for practical Watson-Crick membership testing and is a good basis for improvement the efficiency of the algorithm in the future.