Algorithms for Checking Intersection Non-emptiness of Regular Expressions

Weihao Su, Rongchen Li, Chengyao Peng, Haiming Chen

Abstract: The intersection non-emptiness problem of regular languages is one of the most classical and fundamental decision problems in formal language theory, which plays an important role in many areas. Because of its wide applications, the efficiency of the algorithms becomes particularly crucial. In practice, it is quite common that automata have large numbers of states, therefore the explicit construction of automata may incur significant costs in terms of both time and space, significantly impacting the performance of the related programs. To overcome this challenge, in this paper, we present four efficient algorithms for checking the intersection of regular expressions without the need for automata construction. Our algorithms employ lazy evaluation strategies to simulate intersection non-emptiness checking on automata to avoid constructing automata. They also use automata with fewer states to reduce the state complexity. We conducted experiments and compared our results with seven state-of-the-art tools. The results show significant advantages of our algorithms over existing methods in terms of efficiency and accuracy.