In the process of writing a Turing machine simulator, I decided on a machine representation in ASCII that closely mirrors Turing's original machine tables. I am interested in the formal categorization of the grammar and the simplest type of parser required to implement it, and in a more formal description of same. The grammar is as follows:

<instruction> ::= <ident> "," <symbol> "," <operation> "," <ident> <EOL>
      <ident> ::= <char>
      <symbol ::= <char> | 'None'
  <operation> ::= <movement> | <write> <movement>
      <write> ::= 'P' <char> | 'E'
    <movement ::= 'R' | 'L'

An example Turing machine table written in this grammar is as follows:

b, None, P0R, c
c, None, R,   e
e, None, P1R, f
f, None, R,   b

It is clear to me that since this grammar is expressible in BNF, it must then be at most context-free, but is there a more accurate (more strict) categorization? The lack of left-recursion implies that it could be parsed with a recursive descent parser, but is there a simpler parser that would be capable of this grammar? How would one describe this grammar and its (simplest) associated parser?


1 Answer 1


if you don't count rembering the symbols of previous lines it's a regular language here's the regex as I see it (<char> is translated to [a-z])


use capturing groups as necessary ;)

  • $\begingroup$ So then it's safe to say that the language is regular and the parser need only be a DSM? That's what I suspected, thanks. $\endgroup$ Commented Sep 5, 2011 at 21:07
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    $\begingroup$ @Rein the control of a TM is usually represented as a finite-state machine which characterize regular languages, so you shouldn't be surprised that the grammar you described is regular. $\endgroup$ Commented Sep 6, 2011 at 6:26
  • $\begingroup$ @Artem Good point, although in Turing's later examples he groups instructions by configuration name, which I believe would require a context-free grammar as ratchet freak implied? $\endgroup$ Commented Sep 6, 2011 at 8:12
  • $\begingroup$ @rein what I meant with capturing groups is this I just named it for if you wanted to use the regex parser built into a lot of languages $\endgroup$ Commented Sep 6, 2011 at 8:29
  • $\begingroup$ @ratchet I understand capturing groups. I was referring to your statement, "if you don't count rembering the symbols of previous lines it's a regular language". What if you do need to rememeber the symbols (idents) of previous lines, as Turing's later tables did? $\endgroup$ Commented Sep 6, 2011 at 8:34

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