AP Chapter 12 Vocab

Tape Alphabet

A Turing machine has a tape of infinite length that enables read and write operations to be performed. This is the tape alphabet.

Recognizer

A recognizer is a machine that has a recognizable language. A recognizable language is a language for which there is at least one machine that has it as its language. In lay terms, a language is recognizable if you can think of a machine that'd be able to accept all its strings. Example: L = { abc }. This language is composed only by the word abc. This means that to prove that this language is recognizable, one must build one machine that accepts it. recognizes certain patterns on a tape.

Turing Machine Program

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

State Diagram

A state diagram is a type of diagram used in computer science and related fields to describe the behavior of systems. State diagrams require that the system described is composed of a finite number of states; sometimes, this is indeed the case, while at other times this is a reasonable abstraction.

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

Church-Turing Thesis

In computability theory, the Church-Turing thesis is a hypothesis about the nature of computable functions. It states that a function on the natural numbers is computable by a human being following an algorithm, ignoring resource limitations, if and only if it is computable by a Turing machine.

Halting Problem

In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running or continue to run forever.

Proof by Contradiction

In logic, proof by contradiction is a form of proof, and more specifically a form of indirect proof, that establishes the truth or validity of a proposition. It starts by assuming that the opposite proposition is true, and then shows that such an assumption leads to a contradiction.-- make assumptions then proving it

Turing Award

The ACM A.M. Turing Award is an annual prize given by the Association for Computing Machinery to an individual selected for contributions "of lasting and major technical importance to the computer field"

Unary Representation

Unary numeral system, the simplest numeral system to represent natural numbers.

Turing Machine

a mathematical model of a hypothetical computing machine that can use a predefined set of rules to determine a result from a set of input variables

Uncomputable/Unsolvable

numbers that are well defined, but they still cannot be computed

Computability

the ability to solve a problem in an effective manner. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is closely linked to the existence of an algorithm to solve the problem.