Turing Machines for Dummies - Why Representations Do Matter

Abstract. Various methods exists in the literature for denoting the configuration of a Turing Machine. A key difference is whether the head position is indicated by some integer (mathematical representation) or is specified by writing the machine state next to the scanned tape symbol (intrinsic representation). From a mathematical perspective this will make no difference. However, since Turing Machines are primarily used for proving undecidability and/or hardness results these representations do matter. Based on a number of applications we show that the intrinsic representation should be preferred1 . 1 The Turing Machine model Given the nature of the meeting I expect that the dummies mentioned in my title will not be present in the audience. Still I believe that it is useful to start with a description of the Turing Machine model as we are supposed to know it. The simplest version of the Turing machine is defined in mathematical terms by a tuple M = K, Σ, P, q0, qf , b, ∆ . The...

• Type: Journal
• Year: 2012
• Where: SOFSEM
• Authors: Peter van Emde Boas
• Keywords: Input Symbol, Mathematical Perspective, SOFSEM 2012, Theoretical Computer Science, Turing Machine Model