Let M be the following Turing machine For each statement ind

Let M be the following Turing machine: For each statement indicate whether it is true or false. M accepts all strings containing a 1. M rejects some strings containing a 0. The language accented by M is empty.

Solution

A Turing machine is a general example of a CPU that controls all data manipulation done by a computer, with the canonical machine using sequential memory to store data. More specifically, it is a machine (automaton) capable of enumerating some arbitrary subset of valid strings of an alphabet; these strings are part of a recursively enumerable set.

Assuming a black box, the Turing machine cannot know whether it will eventually enumerate any one specific string of the subset with a given program. This is due to the fact that the halting problem is unsolvable, which has major implications for the theoretical limits of computing.

The Turing machine is capable of processing an unrestricted grammar, which further implies that it is capable of robustly evaluating first-order logic in an infinite number of ways. This is famously demonstrated through lambda calculus.

A Turing machine that is able to simulate any other Turing machine is called a universal Turing machine (UTM, or simply a universal machine). A more mathematically oriented definition with a similar \"universal\" nature was introduced by Alonzo Church, whose work on lambda calculus intertwined with Turing\'s in a formal theory of computation known as the Church–Turing thesis. The thesis states that Turing machines indeed capture the informal notion of effective methods in logic and mathematics, and provide a precise definition of an algorithm or \"mechanical procedure\". Studying their abstract properties yields many insights into computer science and complexity theory.

Physical description[edit]

1) True

2) False

3) True