// Copyright (C) 2009, 2010 Laboratoire de Recherche et Développement
// de l'Epita (LRDE).
//
// This file is part of Spot, a model checking library.
//
// Spot is free software; you can redistribute it and/or modify it
// under the terms of the GNU General Public License as published by
// the Free Software Foundation; either version 2 of the License, or
// (at your option) any later version.
//
// Spot is distributed in the hope that it will be useful, but WITHOUT
// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
// or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public
// License for more details.
//
// You should have received a copy of the GNU General Public License
// along with Spot; see the file COPYING.  If not, write to the Free
// Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
// 02111-1307, USA.

#ifndef SPOT_TGBAALGOS_MINIMIZE_HH
# define SPOT_TGBAALGOS_MINIMIZE_HH

# include "tgba/tgbaexplicit.hh"

namespace spot
{
  // \brief Use the powerset construction to minimize a TGBA.
  //
  // If \a monitor is set of \c false (the default), then the
  // minimized automaton is correct only for properties that belong to
  // the class of "obligation properties".  This algorithm assumes
  // that the given automaton expresses an obligation properties and
  // will return an automaton that is bogus (i.e. not equivalent to
  // the original) if that is not the case.
  //
  // Please see the following paper for a discussion of this
  // technique.
  //
  // \verbatim
  // @InProceedings{	  dax.07.atva,
  //   author	= {Christian Dax and Jochen Eisinger and Felix Klaedtke},
  //   title		= {Mechanizing the Powerset Construction for Restricted
  // 		  Classes of {$\omega$}-Automata},
  //   year		= 2007,
  //   series	= {Lecture Notes in Computer Science},
  //   publisher	= {Springer-Verlag},
  //   volume	= 4762,
  //   booktitle	= {Proceedings of the 5th International Symposium on
  // 		  Automated Technology for Verification and Analysis
  // 		  (ATVA'07)},
  //   editor	= {Kedar S. Namjoshi and Tomohiro Yoneda and Teruo Higashino
  // 		  and Yoshio Okamura},
  //   month		= oct
  // }
  // \endverbatim
  //
  // Dax et al. suggest one way to check whether a property
  // \f$\varphi\f$ expressed as an LTL formula is an obligation:
  // translate the formula and its negation as two automata \f$A_f\f$
  // and \f$A_{\lnot f}\f$, then minimize both automata and check that
  // the two products $\f \mathrm{minimize(A_{\lnot f})\otimes A_f\f$
  // and $\f \mathrm{minimize(A_f)\otimes A_{\lnot f}\f$ are empty.
  // If that is the case, then the minimization was correct.
  //
  // You may also want to check if \$A_f\$ is a safety automaton using
  // the is_safety_automaton() function.  Since safety properties are
  // a subclass of obligation properties, you can apply the
  // minimization without further test.  Note however that this is
  // only a sufficient condition.
  //
  // If \a monitor is set to \c true, the automaton will be converted
  // into minimal deterministic monitor.  All useless SCCs should have
  // been previously removed (using scc_filter() for instance).  Then
  // the automaton will be reduced as if all states where accepting
  // states.
  //
  // For more detail about monitors, see the following paper:
  // \verbatim
  // @InProceedings{	  tabakov.10.rv,
  //   author	= {Deian Tabakov and Moshe Y. Vardi},
  //   title		= {Optimized Temporal Monitors for SystemC{$^*$}},
  //   booktitle	= {Proceedings of the 10th International Conferance on
  // 		  Runtime Verification},
  //   pages		= {436--451},
  //   year		= 2010,
  //   volume	= {6418},
  //   series	= {Lecture Notes in Computer Science},
  //   month		= nov,
  //   publisher	= {Spring-Verlag}
  // }
  // \endverbatim
  // (Note: although the above paper uses Spot, this function did not
  // exist at that time.)
  tgba_explicit* minimize(const tgba* a, bool monitor = false);
}

#endif /* !SPOT_TGBAALGOS_MINIMIZE_HH */