The conceptual development of nondeterminism in theoretical computer science.

摘要

In this essay, I examine the notion of a nondeterministic algorithm from both a conceptual and historical point of view. I argue that the intuitions underwriting nondeterminism in the context of contemporary theoretical computer science cannot be reconciled with the intuitions that originally motivated nondeterminism. I identify four different intuitions about nondeterminism: nondeterminism as evidence for the Church Turing thesis; nondeterminism as a natural reflection of the mathematician's behavior; nondeterminism as a formal, mathematical generalization; and nondeterminism as a physical process. I shall argue that there are irreconcilable tensions among these intuitions and, moreover, that these tensions have not been acknowledged in the conceptual development of theoretical computer science. In fact, a careful review of the received history reveals a number of gaps and discontinuities. For instance, I examine the seminal writings of Turing and argue that the formal introduction of the nondeterminism is to be found there and not, as is often supposed, in the research of the late 1950s and early 1960s. I also examine the period after 1960 and argue that even the more recent developments concerning nondeterminism are hard to reconstruct.;Although I firmly believe that a rigorous philosophical account of nondeterminism is needed, I am not sure that such an account will bring us any closer to a solution to any of the notoriously difficult theoretical problems that turn on the notion of a nondeterministic algorithm. I do believe, however, that a clear conceptual account of nondeterminism will shed light on many long-standing philosophical problems. I conclude by pointing to a number of philosophical questions that resonate with issues raised by the foregoing investigation of nondeterministic algorithms.