sigref.h

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// Author(s): Jeroen Keiren
// Copyright: see the accompanying file COPYING or copy at
// https://github.com/mCRL2org/mCRL2/blob/master/COPYING
//
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
//
 
#ifndef MCRL2_LTS_SIGREF_H
#define MCRL2_LTS_SIGREF_H
 
#include "mcrl2/lts/lts_utilities.h"
 
namespace mcrl2
{
namespace lts
{
 
typedef std::set<std::pair<std::size_t, std::size_t> > signature_t;
 
template < class LTS_T >
class signature
{
protected:
  const LTS_T& m_lts;
 
  std::vector<signature_t> m_sig;
 
public:
  signature(const LTS_T& lts_)
    : m_lts(lts_), m_sig(m_lts.num_states(), signature_t())
  {}
 
  virtual void compute_signature(const std::vector<std::size_t>& partition) = 0;
 
  virtual void quotient_transitions(std::set<transition>& transitions, const std::vector<std::size_t>& partition)
  {
    for(std::vector<transition>::const_iterator i = m_lts.get_transitions().begin(); i != m_lts.get_transitions().end(); ++i)
    {
      transitions.insert(transition(partition[i->from()], i->label(), partition[i->to()]));
    }
  }
 
  virtual const signature_t& get_signature(std::size_t i) const
  {
    return m_sig[i];
  }
};
 
template < class LTS_T >
class signature_bisim: public signature<LTS_T>
{
protected:
  using signature<LTS_T>::m_lts;
  using signature<LTS_T>::m_sig;
 
public:
  signature_bisim(const LTS_T& lts_)
    : signature<LTS_T>(lts_)
  {
    mCRL2log(log::verbose) << "initialising signature computation for strong bisimulation" << std::endl;
  }
 
  virtual void
  compute_signature(const std::vector<std::size_t>& partition)
  {
    // compute signatures
    m_sig = std::vector<signature_t>(m_lts.num_states(), signature_t());
    for(std::vector<transition>::const_iterator i = m_lts.get_transitions().begin(); i != m_lts.get_transitions().end(); ++i)
    {
      m_sig[i->from()].insert(std::make_pair(m_lts.apply_hidden_label_map(i->label()), partition[i->to()]));
    }
  }
 
};
 
template < class LTS_T >
class signature_branching_bisim: public signature<LTS_T>
{
protected:
  using signature<LTS_T>::m_lts;
  using signature<LTS_T>::m_sig;
 
  outgoing_transitions_per_state_t m_prev_transitions;
 
  void insert(const std::vector<std::size_t>& partition, const std::size_t t, const std::size_t label_, const std::size_t block)
  {
    if(m_sig[t].insert(std::make_pair(label_, block)).second)
    {
      // std::pair<outgoing_transitions_per_state_t::const_iterator, outgoing_transitions_per_state_t::const_iterator> pred_range
      //    = m_prev_transitions.equal_range(t);
 
      // for(outgoing_transitions_per_state_t::const_iterator i = pred_range.first; i != pred_range.second; ++i)
      // for(const outgoing_pair_t& p: m_prev_transitions[t])
      for (std::size_t i=m_prev_transitions.lowerbound(t); i<m_prev_transitions.upperbound(t); ++i)
      {
        const outgoing_pair_t& p = m_prev_transitions.get_transitions()[i];
        if(m_lts.is_tau(m_lts.apply_hidden_label_map(label(p))) && partition[t] == partition[to(p)])
        {
          insert(partition, to(p), label_, block);
        }
      }
    }
  }
 
public:
  signature_branching_bisim(const LTS_T& lts_)
    : signature<LTS_T>(lts_),
      m_prev_transitions(lts_.get_transitions(),lts_.num_states(),false)  // transitions stored backward. 
  {
    mCRL2log(log::verbose) << "initialising signature computation for branching bisimulation" << std::endl;
  }
 
  virtual void compute_signature(const std::vector<std::size_t>& partition)
  {
    // compute signatures
    m_sig = std::vector<signature_t>(m_lts.num_states(), signature_t());
    for(std::vector<transition>::const_iterator i = m_lts.get_transitions().begin(); i != m_lts.get_transitions().end(); ++i)
    {
      if (!(m_lts.is_tau(m_lts.apply_hidden_label_map(i->label())) && (partition[i->from()] == partition[i->to()])))
      {
        insert(partition, i->from(), m_lts.apply_hidden_label_map(i->label()), partition[i->to()]);
      }
    }
  }
 
  virtual void quotient_transitions(std::set<transition>& transitions, const std::vector<std::size_t>& partition)
  {
    for(std::vector<transition>::const_iterator i = m_lts.get_transitions().begin(); i != m_lts.get_transitions().end(); ++i)
    {
      if(partition[i->from()] != partition[i->to()] || !m_lts.is_tau(m_lts.apply_hidden_label_map(i->label())))
      {
        transitions.insert(transition(partition[i->from()], m_lts.apply_hidden_label_map(i->label()), partition[i->to()]));
      }
    }
  }
};
 
template < class LTS_T >
class signature_divergence_preserving_branching_bisim: public signature_branching_bisim<LTS_T>
{
protected:
  using signature_branching_bisim<LTS_T>::m_lts;
  using signature_branching_bisim<LTS_T>::m_sig;
  using signature_branching_bisim<LTS_T>::insert;
 
  std::vector<bool> m_divergent;
 
  void compute_tau_sccs()
  {
    std::size_t unused = 1, lastscc = 1;
    std::vector<std::size_t> scc(m_lts.num_states(), 0);
    std::vector<std::size_t> low(m_lts.num_states(), 0);
    std::stack<std::size_t> stack;
    std::stack<std::size_t> sccstack;
 
    // Record forward transition relation sorted by state.
    outgoing_transitions_per_state_t m_lts_succ_transitions(m_lts.get_transitions(),m_lts.num_states(),true);
 
    for (std::size_t i = 0; i < m_lts.num_states(); ++i)
    {
      if (scc[i] == 0)
        stack.push(i);
      while (!stack.empty())
      {
        const std::size_t vi = stack.top();
 
        // Outgoing transitions of vi.
        // std::pair<outgoing_transitions_per_state_t::const_iterator, outgoing_transitions_per_state_t::const_iterator> succ_range
        //  = m_lts_succ_transitions.equal_range(vi);
 
        if (low[vi] == 0 && scc[vi] == 0)
        {
          scc[vi] = unused;
          low[vi] = unused++;
          sccstack.push(vi);
 
          // for (outgoing_transitions_per_state_t::const_iterator t = succ_range.first; t != succ_range.second; ++t)
          // for (const outgoing_pair_t& t: m_lts_succ_transitions[vi]) 
          // for (const outgoing_pair_t& t: m_lts_succ_transitions[vi]) 
          for (std::size_t i=m_lts_succ_transitions.lowerbound(vi); i<m_lts_succ_transitions.upperbound(vi); ++i)
          {
            const outgoing_pair_t& t=m_lts_succ_transitions.get_transitions()[i];
            if ((low[to(t)] == 0) && (scc[to(t)] == 0) && (m_lts.is_tau(m_lts.apply_hidden_label_map(label(t)))))
            {
              stack.push(to(t));
            }
          }
        }
        else
        {
          // for (outgoing_transitions_per_state_t::const_iterator t = succ_range.first; t != succ_range.second; ++t)
          for (std::size_t i=m_lts_succ_transitions.lowerbound(vi); i<m_lts_succ_transitions.upperbound(vi); ++i)
          {
            const outgoing_pair_t& t=m_lts_succ_transitions.get_transitions()[i];
            if ((low[to(t)] != 0) && (m_lts.is_tau(m_lts.apply_hidden_label_map(label(t)))))
              low[vi] = low[vi] < low[to(t)] ? low[vi] : low[to(t)];
          }
          if (low[vi] == scc[vi])
          {
            std::size_t tos, scc_id = lastscc++;
            std::vector<std::size_t> this_scc;
            do
            {
              tos = sccstack.top();
              low[tos] = 0;
              scc[tos] = scc_id;
              sccstack.pop();
              this_scc.push_back(tos);
            }
            while (tos != vi);
 
            // We only consider non-trivial sccs, hence
            // if the scc consists of a single schate, check whether it has a tau-loop
            if(this_scc.size() == 1)
            {
              // for(outgoing_transitions_per_state_t::const_iterator i = succ_range.first; i != succ_range.second; ++i)
              // for (const outgoing_pair_t& i: m_lts_succ_transitions[vi]) 
              for (std::size_t i_=m_lts_succ_transitions.lowerbound(vi); i_<m_lts_succ_transitions.upperbound(vi); ++i_)
              {
                const outgoing_pair_t& i=m_lts_succ_transitions.get_transitions()[i_];
                if(vi == to(i) && m_lts.is_tau(m_lts.apply_hidden_label_map(label(i))))
                {
                  m_divergent[tos] = true;
                  break;
                }
              }
            }
            else
            {
              m_divergent[tos] = true;
            }
          }
          stack.pop();
        }
      }
    }
  }
 
public:
  signature_divergence_preserving_branching_bisim(const LTS_T& lts_)
    : signature_branching_bisim<LTS_T>(lts_),
      m_divergent(lts_.num_states(), false)
  {
    mCRL2log(log::verbose) << "initialising signature computation for divergence preserving branching bisimulation" << std::endl;
    compute_tau_sccs();
  }
 
  virtual void compute_signature(const std::vector<std::size_t>& partition)
  {
    // compute signatures
    m_sig = std::vector<signature_t>(m_lts.num_states(), signature_t());
    for(std::vector<transition>::const_iterator i = m_lts.get_transitions().begin(); i != m_lts.get_transitions().end(); ++i)
    {
      if(!(partition[i->from()] == partition[i->to()] && m_lts.is_tau(m_lts.apply_hidden_label_map(i->label())))
         || m_divergent[i->to()])
      {
        insert(partition, i->from(), m_lts.apply_hidden_label_map(i->label()), partition[i->to()]);
      }
    }
  }
 
  virtual void quotient_transitions(std::set<transition>& transitions, const std::vector<std::size_t>& partition)
  {
    for(std::vector<transition>::const_iterator i = m_lts.get_transitions().begin(); i != m_lts.get_transitions().end(); ++i)
    {
      if(!(partition[i->from()] == partition[i->to()] && m_lts.is_tau(m_lts.apply_hidden_label_map(i->label())))
         || m_sig[i->from()].find(std::make_pair(m_lts.apply_hidden_label_map(i->label()), partition[i->to()])) != m_sig[i->from()].end())
      {
        transitions.insert(transition(partition[i->from()], m_lts.apply_hidden_label_map(i->label()), partition[i->to()]));
      }
    }
  }
};
 
 
template < class LTS_T, typename Signature >
class sigref
{
 
protected:
  std::vector<std::size_t> m_partition;
 
  std::size_t m_count;
 
  LTS_T& m_lts;
 
  Signature m_signature;
 
  std::string print_sig(const signature_t& sig)
  {
    std::stringstream os;
    os << "{ ";
    for(signature_t::const_iterator i = sig.begin(); i != sig.end() ; ++i)
    {
      os << " (" << pp(m_lts.action_label(i->first)) << ", " << i->second << ") ";
    }
    os << " }";
    return os.str();
  }
 
  void compute_partition()
  {
    std::size_t count_prev = m_count;
    std::size_t iterations = 0;
 
    sort_transitions(m_lts.get_transitions(), m_lts.hidden_label_set(), mcrl2::lts::lbl_tgt_src);
 
    do
    {
      mCRL2log(log::verbose) << "Iteration " << iterations
                                       << " currently have " << m_count << " blocks" << std::endl;
 
      m_signature.compute_signature(m_partition);
 
      count_prev = m_count;
 
      // Map signatures to block numbers
      std::map<signature_t, std::size_t> hashtable;
      m_count = 0;
      for(std::size_t i = 0; i < m_lts.num_states(); ++i)
      {
        if(hashtable.find(m_signature.get_signature(i)) == hashtable.end())
        {
          mCRL2log(log::debug) << "Adding block for signature " << print_sig(m_signature.get_signature(i)) << std::endl;
          hashtable[m_signature.get_signature(i)] = m_count++;
        }
      }
 
      // Map states to block numbers
      for(std::size_t i = 0; i < m_lts.num_states(); ++i)
      {
        m_partition[i] = hashtable[m_signature.get_signature(i)];
      }
 
      ++iterations;
 
    } while (count_prev != m_count);
 
    mCRL2log(log::verbose) << "Done after " << iterations << " iterations with " << m_count << " blocks" << std::endl;
  }
 
  void quotient()
  {
    // Assign the reduced LTS
    m_lts.set_num_states(m_count);
    m_lts.set_initial_state(m_partition[m_lts.initial_state()]);
 
    // Compute quotient transitions
    // implemented in the signature class because it differs per equivalence.
    std::set<transition> transitions;
    m_signature.quotient_transitions(transitions, m_partition);
 
    // Set quotient transitions
    m_lts.clear_transitions();
    for(std::set<transition>::const_iterator i = transitions.begin(); i != transitions.end(); ++i)
    {
      m_lts.add_transition(*i);
    }
  }
 
public:
  sigref(LTS_T& lts_)
    : m_partition(std::vector<std::size_t>(lts_.num_states(), 0)),
      m_count(0),
      m_lts(lts_),
      m_signature(lts_)
  {}
 
  void run()
  {
    // No need for state labels in the reduced LTS.
    m_lts.clear_state_labels();
    compute_partition();
    quotient();
  }
};
 
} // namespace lts
} // namespace mcrl2
 
#endif // MCRL2_LTS_SIGREF_H