Invitation to Computer Science Chapter-12

recognizer

A Turing machine that decides whether the string of characters initially on its tape matches a certain pattern

uncomputable / unsolvable

A problem for which no solution algorithm exists

Turing machine program

A set of Turing machine instructions that allows a Turing machine to carry out a certain task

parity bit

A single bit added to the end of a binary string to set the total number of 1s, including the parity bit, to an even or odd number (even or odd parity bit), which allows detection of single-bit errors in transmission

Turing machine

A theoretical model of a computing agent in which symbols are written in cells of a hypothetical infinite tape and are read and changed by a read/write unit according to the input symbol, the state of the read/write head, and the set of rules for the Turing machine

state diagram

A visual representation of a Turing machine algorithm

proof by contradiction

Assume the opposite of what you want to prove and follow the logical consequences until you reach a contradiction, thereby showing that your assumption is incorrect

halting problem

Decide, given any collection of Turing machine instructions together with any initial tape contents, whether that Turing machine will ever halt if started on that tape

Turing machine instruction

Given the current tape symbol and the state of the read/write unit, describes the symbol to write, the next state, and the direction of move of the read/write unit

computability

That which can be done by symbol manipulation algorithms

tape alphabet

The allowable symbols that can be written on a Turing machine tape

Turing Award

The most prestigious technical award given by the Association for Computing Machinery; it is for "contributions of lasting and major technical importance to the computer field"

Church-Turing thesis

The thesis that if there exists an algorithm to do a symbol manipulation task, then there exists a Turing machine to do that task

unary representation

Using only one symbol to represent whole numbers