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The definition of the set of allowable operations used for computation and their respective costs. Some examples of models include Turing machines, recursive functions, lambda calculus, and production systems.

6 votes
1 answer
818 views

A model of computation vs an abstract machine

Wikipedia says A model of computation is a formal description of a particular type of computational process. The description often takes the form of an abstract machine that is meant to perform …
Tim's user avatar
  • 5,015
5 votes
5 answers
607 views

Can we use domains other than the naturals in computability theory?

I wonder why people assume the domain of a computable function is $\mathbb N$? For example, in Wikipedia. Can its domain be any countable set rather than $\mathbb N$? Can its domain be an uncountabl …
Tim's user avatar
  • 5,015
2 votes
2 answers
717 views

How does an automaton model a computer or something else?

An automaton, as I have seen so far, is used to tell if a string belongs to the language that the automaton recognizes. This is determined by the final state of the automaton running on the string as …
Tim's user avatar
  • 5,015
8 votes
2 answers
3k views

Models of computation: the arithmetic model, Turing machine (and ...)

How is an arithmetic model defined? What relations are between it and Turing machine? Are they equivalent in some sense? Is it true that in the arithmetic model of computation, the basic arithm …
Tim's user avatar
  • 5,015
3 votes
3 answers
916 views

Are partial recursive functions analogous to recursive languages or r.e. languages?

From Ullman and Hopcroft's Introduction to Automata Theory, Language, and Computation 1ed 1979: The assumption that the intuitive notion of "computable function" can be identified with the clas …
Tim's user avatar
  • 5,015
0 votes
2 answers
234 views

Can other models of computation equivalent to Turing machines also recognize the same langua...

There are other models of computation equivalent to Turing machines in terms of computability. Turing machines also recognize recursively enumerable languages. My questions are Do other models of …
Tim's user avatar
  • 5,015
9 votes
3 answers
4k views

Differences between programming model and programming paradigm?

What is the relation and difference between a programming model and a programming paradigm? (especially when talking about the programming model and the programming paradigm for a programming languag …
Tim's user avatar
  • 5,015
2 votes
2 answers
927 views

Are nondeterministic algorithm and randomized algorithms algorithms on a deterministic Turin...

An algorithm on an abstract machine is a finite sequence of operations of the machine. (Correct me if I am not correct.) However, there are different kind of algorithms, such as deterministic, non-de …
Tim's user avatar
  • 5,015
36 votes
6 answers
15k views

Differences and relationships between randomized and nondeterministic algorithms?

What differences and relationships are between randomized algorithms and nondeterministic algorithms? From Wikipedia A randomized algorithm is an algorithm which employs a degree of randomness …
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