Computation and Logic [DRAFT]
Created at 2016-11-04T20:34:47.000Z

Computation

  • Mathematical models of computation

    • regular expression = finite deterministic automaton
    • variants of grammer class
    • variants of automaton (push-down)
    • (primitive) recursive functions
    • Turing machine
    • Lambda calculus
  • defining a model of computation means

    • defining a syntax of program
    • which means it introduces a set of programs definable within a model
    • defining a semantic of each program
    • subset of some mathematical entity
  • each computation model defines a set of programs"class" of problem "domains
    • countable domain -> two value domain
    • e.g. regular expression (stream processing, generally)
    • countable domain -> countable output domain
    • e.g. integer arithmetic
    • uncountable domain -> uncountable domain
    • e.g. floating arithmetic
    • ...probabilistic variant or whatever interesting ...

Logic

  • defining a logic means:
    • defining a syntax (hopefully "encodable" to an input of program of some computation model)
    • syntax of formula
    • suntax of rules
    • defining a semantics (interpretation to domains (input is formula (which is countable) and output is validity (which is 2-value)))

Interesting Problem

  • given:
    • some computation model
    • some logic
  • then find a program (definable within the given computation model) which does:
      -

related work

  • where the heck "complexity" formalism come from?