CHAPTER 3 - Machine-Independent Complexity Theory

Abstract

This chapter discusses machine-independent complexity theory. The familiar measures of computational complexity are time and space. Time is considered as the number of discrete steps in a computation, and space as the number of distinct storage locations accessed by the instructions of the computation. The machines consist of a finite-state program with access to an input tape and a single storage tape. Recorded on the input tape is an input word, a nonnull, finite string of characters from some finite input alphabet. Recorded on the storage tape is a string of characters from the fixed, binary alphabet. The initial content of the storage tape is the trivial word 0 of length 1. A separate tape head is maintained in some position, initially the leftmost one, on each of the two tapes. The finite-state program consists of a finite set of states, one of which is designated as the initial one, and a finite function indicating how each next computational action depends on the visible display of the current total state of the entire machine.