Efficient Simulation of Forward-Branching Systems with Constructor Systems

Strongly sequential constructor systems admit a very efficient algorithm to compute normal forms. Thatte found a transformation that allows us to simulate any orthogonal system with a constructor system. Unfortunately, this transformation does not generally preserve strong sequentiality. On the other hand, the class of forward-branching systems contains the class of strongly sequential constructor systems. Moreover, it admits a reduction algorithm similar to the reduction algorithm of the strongly sequential constructor class, but less efficient on the entire class of forward-branching systems. In this article, we present a new transformation which transforms any forward-branching system into a strongly sequential constructor system. The size of the system increases only modestly over that of the original one in many practical situations. We give an algorithm for this transformation and we prove its correctness and completeness. The new system is then proved to be equivalent to the input system, with respect to the behavior and the semantics. We then give a new transformation algorithm which increases the size of the system only linearly.