Uma abordagem quântica para o uso de expressões regulares.

Abstract

Regular expressions (ER) are abstract concepts from Computing Theory widely used in text processing and pattern matching tasks applied in numerous areas, such as, computational biology, signal processing, text retrieving, handwriting recognition, pattern recognition, etc. The classical approaches for their use have two phases: i) transformation from regular expression to finite automata, where the automata can be deterministic (AFD) or non-deterministic (AFN); and ii) automata implementation (codification and simulation) in classical hardware. However, both phases contain inefficiencies related to time or space consumed in their run. This work proposes a quantum approach alternative to the classical ones for regular expression usage. In the proposed approach, the transformation phase is divided into two steps: the classical conversion ER-AFN continues and it is introduced the transformation from AFN to quantum finite automata (AFQ), by using the algorithm developed and presented in this work. This algorithm uses an AFQ model that recognizes the regular language classes, the AFQ Ancilla model. The transformation is carried out in polynomial time and it preserves the AFN’s number of states, eliminating both the memory inefficiency resulting from AFN-AFD classical conversion, and the later minimization need. In automata implementation phase, it is proposed a framework to describe a quantum finite automata through the quantum circuits language, using a polynomial number of gates proportional to automata number of states and input word size.