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op_obserververification.cpp

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00001 /** @file op_obserververification.cpp 
00002 
00003 Methods to verify the obsrver condition for natural projections.
00004 The observer condition is, e.g., defined in 
00005 K. C. Wong and W. M. Wonham, “Hierarchical control of discrete-event
00006 systems,” Discrete Event Dynamic Systems: Theory and Applications, 1996.
00007 In addition, methods to verify output control consistency (OCC) and 
00008 local control consistency (LCC) are provided. See for example
00009 K. Schmidt and C. Breindl, "On Maximal Permissiveness of Hierarchical and Modular Supervisory
00010 Control Approaches for Discrete Event Systems," Workshop on Discrete Event Systems, 2008. 
00011 */
00012 
00013 /* FAU Discrete Event Systems Library (libfaudes)
00014 
00015    Copyright (C) 2006  Bernd Opitz
00016    Exclusive copyright is granted to Klaus Schmidt
00017 
00018    This library is free software; you can redistribute it and/or
00019    modify it under the terms of the GNU Lesser General Public
00020    License as published by the Free Software Foundation; either
00021    version 2.1 of the License, or (at your option) any later version.
00022 
00023    This library is distributed in the hope that it will be useful,
00024    but WITHOUT ANY WARRANTY; without even the implied warranty of
00025    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
00026    Lesser General Public License for more details.
00027 
00028    You should have received a copy of the GNU Lesser General Public
00029    License along with this library; if not, write to the Free Software
00030    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA */
00031 #include "op_obserververification.h"
00032 
00033 
00034 using namespace std;
00035 
00036 namespace faudes {
00037 
00038 bool IsObs(const Generator& rLowGen, const EventSet& rHighAlph){
00039   OP_DF("IsObs(" << rLowGen.Name() << "," << rHighAlph.Name() << ")");
00040   // Initialization of variables
00041   EventSet newHighAlph = rHighAlph;
00042   EventSet controllableEvents;
00043   map<Transition,Idx> mapChangedTrans;
00044   Generator genDyn(rLowGen);
00045   map<Transition,Transition> mapChangedTransReverse;
00046   vector<Idx> newPartitions;
00047   map<Idx,Idx> mapStateToPartition;
00048   map<Idx, EventSet> mapRelabeledEvents;
00049   // One step of the observer algorithm: A dynamic system is computed that fulfills the one-step observer condition. 
00050   // if the result is equal to the original generator, then the natural projection on the high-level alphabet fulfills the observer property
00051   calculateDynamicSystemClosedObs(rLowGen, newHighAlph, genDyn);
00052   calculateDynamicSystemObs(rLowGen, newHighAlph, genDyn);
00053   Generator genPart;
00054   // compute coarsest quasi-congruence on the dynamic system
00055   calcBisimulation(genDyn, mapStateToPartition, genPart, newPartitions);
00056   // Extend the high-level alphabet according to the algorithm of Lei
00057         ExtendHighAlphabet(rLowGen, newHighAlph, mapStateToPartition);
00058   // return the result of the event extension
00059   return newHighAlph == rHighAlph;
00060 
00061 }
00062 
00063 bool IsMSA(const Generator& rLowGen, const EventSet& rHighAlph){
00064   OP_DF("IsMSA(" << rLowGen.Name() << "," << rHighAlph.Name() << ")");
00065   // Initialization of variables
00066   EventSet newHighAlph = rHighAlph;
00067   EventSet controllableEvents;
00068   map<Transition,Idx> mapChangedTrans;
00069   Generator genDyn(rLowGen);
00070   map<Transition,Transition> mapChangedTransReverse;
00071   vector<Idx> newPartitions;
00072   map<Idx,Idx> mapStateToPartition;
00073   map<Idx, EventSet> mapRelabeledEvents;
00074   // One step of the observer algorithm: A dynamic system is computed that fulfills the one-step observer condition. 
00075   // if the result is equal to the original generator, then the natural projection on the high-level alphabet fulfills the observer property
00076   calculateDynamicSystemClosedObs(rLowGen, newHighAlph, genDyn);
00077         calculateDynamicSystemMSA(rLowGen, newHighAlph, genDyn);
00078   Generator genPart;
00079   // compute coarsest quasi-congruence on the dynamic system
00080   calcBisimulation(genDyn, mapStateToPartition, genPart, newPartitions);
00081   // Extend the high-level alphabet according to the algorithm of Lei
00082         ExtendHighAlphabet(rLowGen, newHighAlph, mapStateToPartition);
00083   // return the result of the event extension
00084   return newHighAlph == rHighAlph;
00085 
00086 }
00087 
00088 bool IsOCC(const System& rLowGen, const EventSet& rHighAlph){
00089   OP_DF("IsOCC(" << rLowGen.Name() << "," << rHighAlph.Name() << ")");
00090   EventSet controllableEvents = rLowGen.ControllableEvents();
00091   // call the function that implements the algorithm
00092   return IsOCC(rLowGen, controllableEvents, rHighAlph);
00093 }
00094 
00095 bool IsOCC(const Generator& rLowGen, const EventSet& rControllableEvents, const EventSet& rHighAlph){
00096   OP_DF("IsOCC(" << rLowGen.Name() << "," << rHighAlph.Name() << ")");
00097   //helpers:
00098   StateSet::Iterator stIt, stEndIt;
00099   stIt = rLowGen.StatesBegin();
00100   stEndIt = rLowGen.StatesEnd();
00101   TransSet::Iterator tIt, tEndIt;
00102   // iteration over all states of rLowGen. If there is an uncontrollable feasible high-level event, backward reachability is conducted to determine if OCC holds. 
00103   for( ; stIt != stEndIt; stIt++){
00104     tIt = rLowGen.TransRelBegin(*stIt);
00105     tEndIt = rLowGen.TransRelEnd(*stIt);
00106     for( ; tIt != tEndIt; tIt++){
00107       if(rHighAlph.Exists(tIt->Ev) && !rControllableEvents.Exists(tIt->Ev) ){
00108         // check if all local backward paths are uncontrollable
00109         bool uncontrollable = backwardVerificationOCC(rLowGen, rControllableEvents, rHighAlph, *stIt);
00110         // if not all paths are uncontrollable, OCC is violated
00111         if(uncontrollable == false)
00112           return false;
00113         // otherwise, go to the next state
00114         else
00115           break;
00116       }
00117     }
00118   }
00119   return true;
00120 }
00121 
00122 bool backwardVerificationOCC(const Generator& rLowGen, const EventSet& rControllableEvents, const EventSet& rHighAlph, Idx currentState){
00123   OP_DF("backwardVerificationOCC(" << rLowGen.Name() << "," << rControllableEvents.Name() << "," << rHighAlph.Name() << "," << currentState << ")");
00124   // reverse transition relation
00125   TransSetX2EvX1 tset_X2EvX1;
00126   rLowGen.TransRel(tset_X2EvX1);
00127   TransSetX2EvX1::Iterator tsIt, tsEndIt;
00128   // todo list
00129   std::stack<Idx> todo;
00130   // algorithm: the locally backwards reachable states from current staet are 
00131   // evaluated. If a controllable event is found, OCC is violated.
00132   StateSet doneStates;
00133   doneStates.Insert(currentState);
00134   todo.push(currentState);
00135   // the local reachability is evaluated until no new state is found
00136   while( !todo.empty() ){
00137     const Idx current = todo.top();
00138     todo.pop();
00139     tsIt = tset_X2EvX1.BeginByX2(current);
00140     tsEndIt = tset_X2EvX1.EndByX2(current);
00141     for(; tsIt != tsEndIt; tsIt++){
00142       // if the current transition is labeled with a high-level evnet
00143       // it is skipped
00144       if(rHighAlph.Exists(tsIt->Ev) )
00145         continue;
00146       // if the current transition is controllable, OCC is violated
00147       else if( rControllableEvents.Exists(tsIt->Ev) )
00148         return false;
00149       else if( !doneStates.Exists(tsIt->X1) ){
00150         todo.push(tsIt->X1);
00151         doneStates.Insert(tsIt->X1);
00152       }
00153     }
00154   }
00155   return true;
00156 }
00157 
00158 
00159 bool IsLCC(const System& rLowGen, const EventSet& rHighAlph){
00160   OP_DF("IsLCC(" << rLowGen.Name() << "," << rHighAlph.Name() << ")");
00161   EventSet controllableEvents = rLowGen.ControllableEvents();
00162   // call the function that implements the algorithm
00163   return IsLCC(rLowGen, controllableEvents, rHighAlph);
00164 }
00165 
00166 bool IsLCC(const Generator& rLowGen, const EventSet& rControllableEvents, const EventSet& rHighAlph){
00167   OP_DF("IsLCC(" << rLowGen.Name() << "," << rHighAlph.Name() << ")");
00168   // reverse transition relation
00169   TransSetX2EvX1 tset_X2EvX1;
00170   rLowGen.TransRel(tset_X2EvX1);
00171   //helpers:
00172   StateSet::Iterator stIt, stEndIt;
00173   stIt = rLowGen.StatesBegin();
00174   stEndIt = rLowGen.StatesEnd();
00175   TransSet::Iterator tIt, tEndIt;
00176   StateSet doneStates;
00177   map<Idx, bool> localStatesMap;
00178   map<Idx, bool>::const_iterator lsIt, lsEndIt;
00179   // iteration over all states of rLowGen. If there is an uncontrollable feasible high-level event, backward reachability is conducted to determine if LCC holds. 
00180   for( ; stIt != stEndIt; stIt++){
00181     tIt = rLowGen.TransRelBegin(*stIt);
00182     tEndIt = rLowGen.TransRelEnd(*stIt);
00183     for( ; tIt != tEndIt; tIt++){
00184       if(rHighAlph.Exists(tIt->Ev) && !rControllableEvents.Exists(tIt->Ev) ){
00185         doneStates.Clear();
00186         localStatesMap.clear();
00187         localStatesMap[*stIt] = false;
00188         doneStates.Insert(*stIt);
00189         // check if for all backward reachable states, a local uncontrollable backward paths exists
00190         backwardVerificationLCC(tset_X2EvX1, rControllableEvents, rHighAlph, *stIt, *stIt, false, localStatesMap, doneStates);
00191         // if for some state, all paths are controllable, LCC is violated
00192         lsIt = localStatesMap.begin();
00193         lsEndIt = localStatesMap.end();
00194         for( ; lsIt != lsEndIt; lsIt++){
00195           // if there is a state with only controllable paths, LCC is violated
00196           if(lsIt->second == true)
00197             return false;
00198         }
00199         // the evaluation for the current state is finished
00200         break;
00201       }
00202     }
00203   }
00204   return true;
00205 }
00206 
00207 
00208 void backwardVerificationLCC(const TransSetX2EvX1& rTransSetX2EvX1, const EventSet& rControllableEvents, const EventSet& rHighAlph, Idx exitState, Idx currentState, bool controllablePath, map<Idx, bool>& rLocalStatesMap, StateSet& rDoneStates){
00209   OP_DF("backwardVerificationLCC(rTransSetX2EvX1," << rControllableEvents.Name() << "," << rHighAlph.Name() << "," << exitState << "," << currentState << "," << controllablePath << ",rExitLocalStatesMap, rDoneStates)");
00210     // go along all backward transitions. Discard the goal state if it is reached via a high-level event or if it is in the rDoneStates and 
00211     // the controllability properties of the state do not change on the current path
00212     
00213   // helpers
00214   TransSetX2EvX1::Iterator tsIt, tsEndIt;
00215   tsIt = rTransSetX2EvX1.BeginByX2(currentState);
00216   tsEndIt = rTransSetX2EvX1.EndByX2(currentState);
00217   bool currentControllablePath;
00218   // we iterate over all backward transitions of the currentState to establish backward reachability
00219   for( ;tsIt != tsEndIt; tsIt++){
00220       // states reachable via a high-level event are not in the local backward reach and the controllability property of the current exitState does not change
00221     if( !rHighAlph.Exists(tsIt->Ev) && tsIt->X1 != exitState){
00222       // if the state has not been visited, yet, the controllability of the current path are set in the rExitLocalStatesMap
00223               if( !rDoneStates.Exists(tsIt->X1) ){
00224         rDoneStates.Insert(tsIt->X1);
00225         // the path is uncontrollable if the current transition has an uncontrollable event or the path was already uncontrollable
00226         currentControllablePath = rControllableEvents.Exists(tsIt->Ev) || controllablePath;
00227         rLocalStatesMap[tsIt->X1] = currentControllablePath;
00228         // as the state has not been visited, yet, it is subject to a new backward reachability
00229                     backwardVerificationLCC(rTransSetX2EvX1, rControllableEvents, rHighAlph, exitState, tsIt->X1, currentControllablePath, rLocalStatesMap, rDoneStates);
00230       }
00231       else{ // for an existing state, the controllability value can change from controllable to uncontrollable (if 
00232         // a new uncontrollable path has been found). It is important to note, that the LCC condition implies that
00233         // if there is one uncontrollable path, then the state is flagged uncontrollable except for the case of the 
00234         // given exitState that is always uncontrollable
00235         currentControllablePath = rControllableEvents.Exists(tsIt->Ev) || controllablePath;
00236         if(rLocalStatesMap[tsIt->X1] != currentControllablePath && currentControllablePath == false){
00237           rLocalStatesMap[tsIt->X1] = false;
00238           // as the controllabiity attribute of the current state changed it is subject to a new backward reachability
00239                           backwardVerificationLCC(rTransSetX2EvX1, rControllableEvents, rHighAlph, exitState, tsIt->X1, false, rLocalStatesMap, rDoneStates);
00240         }
00241       }
00242     }
00243   }
00244 }
00245 
00246 
00247 
00248  
00249 
00250 
00251 }// namespace faudes

libFAUDES 2.20d --- 2011.04.26 --- c++ source docu by doxygen