#+TITLE: =ltlgrind=
#+EMAIL spot@lrde.epita.fr
#+OPTIONS: H:2 num:nil toc:t
#+LINK_UP: tools.html

This tool lists formulas that are similar to but simpler than a given
formula by applying simple mutations to it, like removing operands or
operators. This is meant to be used with ltlcross to simplify a
formula that caused a problem before trying to debug it (see also
=ltlcross --grind=FILENAME=).

Here is a list of the different kind of mutations that can be applied:

#+BEGIN_SRC sh :results verbatim :exports results
ltlgrind --help | sed -n '/Transformation rules:/,/^$/p' | sed '1d;$d'
#+END_SRC

#+RESULTS:
#+begin_example
      --ap-to-const          atomic propositions are replaced with true/false
      --remove-multop-operands   remove one operand from multops
      --remove-one-ap        all occurrences of an atomic proposition are
                             replaced with another atomic proposition used in
                             the formula
      --remove-ops           replace unary/binary operators with one of their
                             operands
      --rewrite-ops          rewrite operators that have a semantically simpler
                             form: a U b becomes a W b, etc.
      --simplify-bounds      on a bounded unary operator, decrement one of the
                             bounds, or set min to 0 or max to unbounded.
      --split-ops            when an operator can be expressed as a
                             conjunction/disjunction using simpler operators,
                             each term of the conjunction/disjunction is a
                             mutation. e.g. a <-> b can be written as ((a & b)
                             | (!a & !b)) or as ((a -> b) & (b -> a)) so those
                             four terms can be a mutation of a <-> b
#+end_example

By default, all rules are applied. But if one or more rules are
specified, only those will be applied.

#+BEGIN_SRC sh :results verbatim :exports both
ltlgrind -f 'a U G(b <-> c)' --split-ops --rewrite-ops --remove-ops
#+END_SRC

#+RESULTS:
#+begin_example
a
G(b <-> c)
a W G(b <-> c)
a U (b <-> c)
a U Gb
a U Gc
a U G(b -> c)
a U G(c -> b)
a U G(b & c)
a U G(!b & !c)
#+end_example

The idea behind this tool is that when a bogus algorithm is found with
=ltlcross=, you probably want to debug it using a smaller formula than
the one found by =ltlcross=. So you would give the formula found by
=ltlcross= as an argument to =ltlgrind= and then use the resulting
mutations as an new input for =ltlcross=. It might report an error on
one of the mutation, which is guaranteed to be simpler than the
initial formula. The process can then be repeated until no error is
reported by =ltlcross=.

Since the whole process can become quite tedious, it can be done
automatically by calling =ltlcross= with the =--grind=FILENAME=
argument.

* Miscellaneous options
** =--sort=
  Formulas are outputted from the shortest to the longest one. The
  length of a formula is the number of atomic propositions, constants
  and operators occuring in the formula.
** =-m N=, =--mutations=N=
   This option is used to specify the number of mutations to be
   applied to the formula. This is like calling ltlgrind on its own
   output several times, except for the fact that, when called on
   several formulas, ltlgrind doesn't handle duplicates.