/**
* Prob0 precomputation algorithm. i.e. determine the states of an STPG which, with min/max
* probability 0, reach a state in {@code target}, while remaining in those in @{code remain}.
* {@code min}=true gives Prob0E, {@code min}=false gives Prob0A.
*
* @param stpg The STPG
* @param remain Remain in these states (optional: null means "all")
* @param target Target states
* @param min1 Min or max probabilities for player 1 (true=lower bound, false=upper bound)
* @param min2 Min or max probabilities for player 2 (true=min, false=max)
*/
public BitSet prob0(STPG stpg, BitSet remain, BitSet target, boolean min1, boolean min2) {
int n, iters;
BitSet u, soln, unknown;
boolean u_done;
long timer;
// Start precomputation
timer = System.currentTimeMillis();
if (verbosity >= 1)
mainLog.println(
"Starting Prob0 (" + (min1 ? "min" : "max") + (min2 ? "min" : "max") + ")...");
// Special case: no target states
if (target.cardinality() == 0) {
soln = new BitSet(stpg.getNumStates());
soln.set(0, stpg.getNumStates());
return soln;
}
// Initialise vectors
n = stpg.getNumStates();
u = new BitSet(n);
soln = new BitSet(n);
// Determine set of states actually need to perform computation for
unknown = new BitSet();
unknown.set(0, n);
unknown.andNot(target);
if (remain != null) unknown.and(remain);
// Fixed point loop
iters = 0;
u_done = false;
// Least fixed point - should start from 0 but we optimise by
// starting from 'target', thus bypassing first iteration
u.or(target);
soln.or(target);
while (!u_done) {
iters++;
// Single step of Prob0
stpg.prob0step(unknown, u, min1, min2, soln);
// Check termination
u_done = soln.equals(u);
// u = soln
u.clear();
u.or(soln);
}
// Negate
u.flip(0, n);
// Finished precomputation
timer = System.currentTimeMillis() - timer;
if (verbosity >= 1) {
mainLog.print("Prob0 (" + (min1 ? "min" : "max") + (min2 ? "min" : "max") + ")");
mainLog.println(" took " + iters + " iterations and " + timer / 1000.0 + " seconds.");
}
return u;
}
/**
* Compute next=state probabilities. i.e. compute the probability of being in a state in {@code
* target} in the next step.
*
* @param stpg The STPG
* @param target Target states
* @param min1 Min or max probabilities for player 1 (true=lower bound, false=upper bound)
* @param min2 Min or max probabilities for player 2 (true=min, false=max)
*/
public ModelCheckerResult computeNextProbs(STPG stpg, BitSet target, boolean min1, boolean min2)
throws PrismException {
ModelCheckerResult res = null;
int n;
double soln[], soln2[];
long timer;
timer = System.currentTimeMillis();
// Store num states
n = stpg.getNumStates();
// Create/initialise solution vector(s)
soln = Utils.bitsetToDoubleArray(target, n);
soln2 = new double[n];
// Next-step probabilities
stpg.mvMultMinMax(soln, min1, min2, soln2, null, false, null);
// Return results
res = new ModelCheckerResult();
res.soln = soln2;
res.numIters = 1;
res.timeTaken = timer / 1000.0;
return res;
}
/**
* Compute expected reachability rewards. i.e. compute the min/max reward accumulated to reach a
* state in {@code target}.
*
* @param stpg The STPG
* @param rewards The rewards
* @param target Target states
* @param min1 Min or max rewards for player 1 (true=min, false=max)
* @param min2 Min or max rewards for player 2 (true=min, false=max)
* @param init Optionally, an initial solution vector (may be overwritten)
* @param known Optionally, a set of states for which the exact answer is known Note: if 'known'
* is specified (i.e. is non-null, 'init' must also be given and is used for the exact values.
*/
public ModelCheckerResult computeReachRewards(
STPG stpg,
STPGRewards rewards,
BitSet target,
boolean min1,
boolean min2,
double init[],
BitSet known)
throws PrismException {
ModelCheckerResult res = null;
BitSet inf;
int i, n, numTarget, numInf;
long timer, timerProb1;
// Start expected reachability
timer = System.currentTimeMillis();
if (verbosity >= 1) mainLog.println("\nStarting expected reachability...");
// Check for deadlocks in non-target state (because breaks e.g. prob1)
stpg.checkForDeadlocks(target);
// Store num states
n = stpg.getNumStates();
// Optimise by enlarging target set (if more info is available)
if (init != null && known != null) {
BitSet targetNew = new BitSet(n);
for (i = 0; i < n; i++) {
targetNew.set(i, target.get(i) || (known.get(i) && init[i] == 0.0));
}
target = targetNew;
}
// Precomputation (not optional)
timerProb1 = System.currentTimeMillis();
inf = prob1(stpg, null, target, !min1, !min2);
inf.flip(0, n);
timerProb1 = System.currentTimeMillis() - timerProb1;
// Print results of precomputation
numTarget = target.cardinality();
numInf = inf.cardinality();
if (verbosity >= 1)
mainLog.println(
"target=" + numTarget + ", inf=" + numInf + ", rest=" + (n - (numTarget + numInf)));
// Compute rewards
switch (solnMethod) {
case VALUE_ITERATION:
res = computeReachRewardsValIter(stpg, rewards, target, inf, min1, min2, init, known);
break;
default:
throw new PrismException("Unknown STPG solution method " + solnMethod);
}
// Finished expected reachability
timer = System.currentTimeMillis() - timer;
if (verbosity >= 1)
mainLog.println("Expected reachability took " + timer / 1000.0 + " seconds.");
// Update time taken
res.timeTaken = timer / 1000.0;
res.timePre = timerProb1 / 1000.0;
return res;
}
/**
* Compute bounded reachability/until probabilities. i.e. compute the min/max probability of
* reaching a state in {@code target}, within k steps, and while remaining in states in @{code
* remain}.
*
* @param stpg The STPG
* @param remain Remain in these states (optional: null means "all")
* @param target Target states
* @param k Bound
* @param min1 Min or max probabilities for player 1 (true=lower bound, false=upper bound)
* @param min2 Min or max probabilities for player 2 (true=min, false=max)
* @param init Initial solution vector - pass null for default
* @param results Optional array of size k+1 to store (init state) results for each step (null if
* unused)
*/
public ModelCheckerResult computeBoundedReachProbs(
STPG stpg,
BitSet remain,
BitSet target,
int k,
boolean min1,
boolean min2,
double init[],
double results[])
throws PrismException {
// TODO: implement until
ModelCheckerResult res = null;
int i, n, iters;
double soln[], soln2[], tmpsoln[];
long timer;
// Start bounded probabilistic reachability
timer = System.currentTimeMillis();
if (verbosity >= 1) mainLog.println("\nStarting bounded probabilistic reachability...");
// Store num states
n = stpg.getNumStates();
// Create solution vector(s)
soln = new double[n];
soln2 = (init == null) ? new double[n] : init;
// Initialise solution vectors. Use passed in initial vector, if present
if (init != null) {
for (i = 0; i < n; i++) soln[i] = soln2[i] = target.get(i) ? 1.0 : init[i];
} else {
for (i = 0; i < n; i++) soln[i] = soln2[i] = target.get(i) ? 1.0 : 0.0;
}
// Store intermediate results if required
// (compute min/max value over initial states for first step)
if (results != null) {
results[0] = Utils.minMaxOverArraySubset(soln2, stpg.getInitialStates(), min2);
}
// Start iterations
iters = 0;
while (iters < k) {
iters++;
// Matrix-vector multiply and min/max ops
stpg.mvMultMinMax(soln, min1, min2, soln2, target, true, null);
// Store intermediate results if required
// (compute min/max value over initial states for this step)
if (results != null) {
results[iters] = Utils.minMaxOverArraySubset(soln2, stpg.getInitialStates(), min2);
}
// Swap vectors for next iter
tmpsoln = soln;
soln = soln2;
soln2 = tmpsoln;
}
// Print vector (for debugging)
// mainLog.println(soln);
// Finished bounded probabilistic reachability
timer = System.currentTimeMillis() - timer;
if (verbosity >= 1) {
mainLog.print(
"Bounded probabilistic reachability ("
+ (min1 ? "min" : "max")
+ (min2 ? "min" : "max")
+ ")");
mainLog.println(" took " + iters + " iterations and " + timer / 1000.0 + " seconds.");
}
// Return results
res = new ModelCheckerResult();
res.soln = soln;
res.lastSoln = soln2;
res.numIters = iters;
res.timeTaken = timer / 1000.0;
res.timePre = 0.0;
return res;
}
/**
* Construct strategy information for min/max reachability probabilities. (More precisely, list of
* indices of player 1 choices resulting in min/max.) (Note: indices are guaranteed to be sorted
* in ascending order.)
*
* @param stpg The STPG
* @param state The state to generate strategy info for
* @param target The set of target states to reach
* @param min1 Min or max probabilities for player 1 (true=min, false=max)
* @param min2 Min or max probabilities for player 2 (true=min, false=max)
* @param lastSoln Vector of probabilities from which to recompute in one iteration
*/
public List<Integer> probReachStrategy(
STPG stpg, int state, BitSet target, boolean min1, boolean min2, double lastSoln[])
throws PrismException {
double val = stpg.mvMultMinMaxSingle(state, lastSoln, min1, min2);
return stpg.mvMultMinMaxSingleChoices(state, lastSoln, min1, min2, val);
}
/**
* Compute reachability probabilities using Gauss-Seidel.
*
* @param stpg The STPG
* @param no Probability 0 states
* @param yes Probability 1 states
* @param min1 Min or max probabilities for player 1 (true=lower bound, false=upper bound)
* @param min2 Min or max probabilities for player 2 (true=min, false=max)
* @param init Optionally, an initial solution vector (will be overwritten)
* @param known Optionally, a set of states for which the exact answer is known Note: if 'known'
* is specified (i.e. is non-null, 'init' must also be given and is used for the exact values.
*/
protected ModelCheckerResult computeReachProbsGaussSeidel(
STPG stpg, BitSet no, BitSet yes, boolean min1, boolean min2, double init[], BitSet known)
throws PrismException {
ModelCheckerResult res;
BitSet unknown;
int i, n, iters;
double soln[], initVal, maxDiff;
boolean done;
long timer;
// Start value iteration
timer = System.currentTimeMillis();
if (verbosity >= 1)
mainLog.println(
"Starting value iteration (" + (min1 ? "min" : "max") + (min2 ? "min" : "max") + ")...");
// Store num states
n = stpg.getNumStates();
// Create solution vector
soln = (init == null) ? new double[n] : init;
// Initialise solution vector. Use (where available) the following in order of preference:
// (1) exact answer, if already known; (2) 1.0/0.0 if in yes/no; (3) passed in initial value;
// (4) initVal
// where initVal is 0.0 or 1.0, depending on whether we converge from below/above.
initVal = (valIterDir == ValIterDir.BELOW) ? 0.0 : 1.0;
if (init != null) {
if (known != null) {
for (i = 0; i < n; i++)
soln[i] = known.get(i) ? init[i] : yes.get(i) ? 1.0 : no.get(i) ? 0.0 : init[i];
} else {
for (i = 0; i < n; i++) soln[i] = yes.get(i) ? 1.0 : no.get(i) ? 0.0 : init[i];
}
} else {
for (i = 0; i < n; i++) soln[i] = yes.get(i) ? 1.0 : no.get(i) ? 0.0 : initVal;
}
// Determine set of states actually need to compute values for
unknown = new BitSet();
unknown.set(0, n);
unknown.andNot(yes);
unknown.andNot(no);
if (known != null) unknown.andNot(known);
// Start iterations
iters = 0;
done = false;
while (!done && iters < maxIters) {
iters++;
// Matrix-vector multiply and min/max ops
maxDiff =
stpg.mvMultGSMinMax(soln, min1, min2, unknown, false, termCrit == TermCrit.ABSOLUTE);
// Check termination
done = maxDiff < termCritParam;
}
// Finished Gauss-Seidel
timer = System.currentTimeMillis() - timer;
if (verbosity >= 1) {
mainLog.print("Value iteration (" + (min1 ? "min" : "max") + (min2 ? "min" : "max") + ")");
mainLog.println(" took " + iters + " iterations and " + timer / 1000.0 + " seconds.");
}
// Non-convergence is an error (usually)
if (!done && errorOnNonConverge) {
String msg = "Iterative method did not converge within " + iters + " iterations.";
msg +=
"\nConsider using a different numerical method or increasing the maximum number of iterations";
throw new PrismException(msg);
}
// Return results
res = new ModelCheckerResult();
res.soln = soln;
res.numIters = iters;
res.timeTaken = timer / 1000.0;
return res;
}
/**
* Compute reachability probabilities using value iteration.
*
* @param stpg The STPG
* @param no Probability 0 states
* @param yes Probability 1 states
* @param min1 Min or max probabilities for player 1 (true=lower bound, false=upper bound)
* @param min2 Min or max probabilities for player 2 (true=min, false=max)
* @param init Optionally, an initial solution vector (will be overwritten)
* @param known Optionally, a set of states for which the exact answer is known Note: if 'known'
* is specified (i.e. is non-null, 'init' must also be given and is used for the exact values.
*/
protected ModelCheckerResult computeReachProbsValIter(
STPG stpg, BitSet no, BitSet yes, boolean min1, boolean min2, double init[], BitSet known)
throws PrismException {
ModelCheckerResult res = null;
BitSet unknown;
int i, n, iters;
double soln[], soln2[], tmpsoln[], initVal;
int adv[] = null;
boolean genAdv, done;
long timer;
// Are we generating an optimal adversary?
genAdv = exportAdv;
// Start value iteration
timer = System.currentTimeMillis();
if (verbosity >= 1)
mainLog.println(
"Starting value iteration (" + (min1 ? "min" : "max") + (min2 ? "min" : "max") + ")...");
// Store num states
n = stpg.getNumStates();
// Create solution vector(s)
soln = new double[n];
soln2 = (init == null) ? new double[n] : init;
// Initialise solution vectors. Use (where available) the following in order of preference:
// (1) exact answer, if already known; (2) 1.0/0.0 if in yes/no; (3) passed in initial value;
// (4) initVal
// where initVal is 0.0 or 1.0, depending on whether we converge from below/above.
initVal = (valIterDir == ValIterDir.BELOW) ? 0.0 : 1.0;
if (init != null) {
if (known != null) {
for (i = 0; i < n; i++)
soln[i] =
soln2[i] = known.get(i) ? init[i] : yes.get(i) ? 1.0 : no.get(i) ? 0.0 : init[i];
} else {
for (i = 0; i < n; i++) soln[i] = soln2[i] = yes.get(i) ? 1.0 : no.get(i) ? 0.0 : init[i];
}
} else {
for (i = 0; i < n; i++) soln[i] = soln2[i] = yes.get(i) ? 1.0 : no.get(i) ? 0.0 : initVal;
}
// Determine set of states actually need to compute values for
unknown = new BitSet();
unknown.set(0, n);
unknown.andNot(yes);
unknown.andNot(no);
if (known != null) unknown.andNot(known);
// Create/initialise adversary storage
if (genAdv) {
adv = new int[n];
for (i = 0; i < n; i++) {
adv[i] = -1;
}
}
// Start iterations
iters = 0;
done = false;
while (!done && iters < maxIters) {
iters++;
// Matrix-vector multiply and min/max ops
stpg.mvMultMinMax(soln, min1, min2, soln2, unknown, false, genAdv ? adv : null);
// Check termination
done = PrismUtils.doublesAreClose(soln, soln2, termCritParam, termCrit == TermCrit.ABSOLUTE);
// Swap vectors for next iter
tmpsoln = soln;
soln = soln2;
soln2 = tmpsoln;
}
// Finished value iteration
timer = System.currentTimeMillis() - timer;
if (verbosity >= 1) {
mainLog.print("Value iteration (" + (min1 ? "min" : "max") + (min2 ? "min" : "max") + ")");
mainLog.println(" took " + iters + " iterations and " + timer / 1000.0 + " seconds.");
}
// Non-convergence is an error (usually)
if (!done && errorOnNonConverge) {
String msg = "Iterative method did not converge within " + iters + " iterations.";
msg +=
"\nConsider using a different numerical method or increasing the maximum number of iterations";
throw new PrismException(msg);
}
// Print adversary
if (genAdv) {
PrismLog out = new PrismFileLog(exportAdvFilename);
for (i = 0; i < n; i++) {
out.println(i + " " + (adv[i] != -1 ? stpg.getAction(i, adv[i]) : "-"));
}
out.println();
}
// Return results
res = new ModelCheckerResult();
res.soln = soln;
res.numIters = iters;
res.timeTaken = timer / 1000.0;
return res;
}
/**
* Compute reachability/until probabilities. i.e. compute the min/max probability of reaching a
* state in {@code target}, while remaining in those in @{code remain}.
*
* @param stpg The STPG
* @param remain Remain in these states (optional: null means "all")
* @param target Target states
* @param min1 Min or max probabilities for player 1 (true=lower bound, false=upper bound)
* @param min2 Min or max probabilities for player 2 (true=min, false=max)
* @param init Optionally, an initial solution vector (may be overwritten)
* @param known Optionally, a set of states for which the exact answer is known Note: if 'known'
* is specified (i.e. is non-null, 'init' must also be given and is used for the exact values.
*/
public ModelCheckerResult computeReachProbs(
STPG stpg,
BitSet remain,
BitSet target,
boolean min1,
boolean min2,
double init[],
BitSet known)
throws PrismException {
ModelCheckerResult res = null;
BitSet no, yes;
int i, n, numYes, numNo;
long timer, timerProb0, timerProb1;
boolean genAdv;
// Check for some unsupported combinations
if (solnMethod == SolnMethod.VALUE_ITERATION
&& valIterDir == ValIterDir.ABOVE
&& !(precomp && prob0)) {
throw new PrismException(
"Precomputation (Prob0) must be enabled for value iteration from above");
}
// Are we generating an optimal adversary?
genAdv = exportAdv;
// Start probabilistic reachability
timer = System.currentTimeMillis();
if (verbosity >= 1) mainLog.println("\nStarting probabilistic reachability...");
// Check for deadlocks in non-target state (because breaks e.g. prob1)
stpg.checkForDeadlocks(target);
// Store num states
n = stpg.getNumStates();
// Optimise by enlarging target set (if more info is available)
if (init != null && known != null) {
BitSet targetNew = new BitSet(n);
for (i = 0; i < n; i++) {
targetNew.set(i, target.get(i) || (known.get(i) && init[i] == 1.0));
}
target = targetNew;
}
// Precomputation
timerProb0 = System.currentTimeMillis();
if (precomp && prob0) {
no = prob0(stpg, remain, target, min1, min2);
} else {
no = new BitSet();
}
timerProb0 = System.currentTimeMillis() - timerProb0;
timerProb1 = System.currentTimeMillis();
if (precomp && prob1 && !genAdv) {
yes = prob1(stpg, remain, target, min1, min2);
} else {
yes = (BitSet) target.clone();
}
timerProb1 = System.currentTimeMillis() - timerProb1;
// Print results of precomputation
numYes = yes.cardinality();
numNo = no.cardinality();
if (verbosity >= 1)
mainLog.println(
"target="
+ target.cardinality()
+ ", yes="
+ numYes
+ ", no="
+ numNo
+ ", maybe="
+ (n - (numYes + numNo)));
// Compute probabilities
switch (solnMethod) {
case VALUE_ITERATION:
res = computeReachProbsValIter(stpg, no, yes, min1, min2, init, known);
break;
case GAUSS_SEIDEL:
res = computeReachProbsGaussSeidel(stpg, no, yes, min1, min2, init, known);
break;
default:
throw new PrismException("Unknown STPG solution method " + solnMethod);
}
// Finished probabilistic reachability
timer = System.currentTimeMillis() - timer;
if (verbosity >= 1)
mainLog.println("Probabilistic reachability took " + timer / 1000.0 + " seconds.");
// Update time taken
res.timeTaken = timer / 1000.0;
res.timeProb0 = timerProb0 / 1000.0;
res.timePre = (timerProb0 + timerProb1) / 1000.0;
return res;
}
/**
* Compute expected reachability rewards using value iteration.
*
* @param stpg The STPG
* @param rewards The rewards
* @param target Target states
* @param inf States for which reward is infinite
* @param min1 Min or max rewards for player 1 (true=min, false=max)
* @param min2 Min or max rewards for player 2 (true=min, false=max)
* @param init Optionally, an initial solution vector (will be overwritten)
* @param known Optionally, a set of states for which the exact answer is known Note: if 'known'
* is specified (i.e. is non-null, 'init' must also be given and is used for the exact values.
*/
protected ModelCheckerResult computeReachRewardsValIter(
STPG stpg,
STPGRewards rewards,
BitSet target,
BitSet inf,
boolean min1,
boolean min2,
double init[],
BitSet known)
throws PrismException {
ModelCheckerResult res;
BitSet unknown;
int i, n, iters;
double soln[], soln2[], tmpsoln[];
boolean done;
long timer;
// Start value iteration
timer = System.currentTimeMillis();
if (verbosity >= 1)
mainLog.println(
"Starting value iteration (" + (min1 ? "min" : "max") + (min2 ? "min" : "max") + ")...");
// Store num states
n = stpg.getNumStates();
// Create solution vector(s)
soln = new double[n];
soln2 = (init == null) ? new double[n] : init;
// Initialise solution vectors. Use (where available) the following in order of preference:
// (1) exact answer, if already known; (2) 0.0/infinity if in target/inf; (3) passed in initial
// value; (4) 0.0
if (init != null) {
if (known != null) {
for (i = 0; i < n; i++)
soln[i] =
soln2[i] =
known.get(i)
? init[i]
: target.get(i) ? 0.0 : inf.get(i) ? Double.POSITIVE_INFINITY : init[i];
} else {
for (i = 0; i < n; i++)
soln[i] =
soln2[i] = target.get(i) ? 0.0 : inf.get(i) ? Double.POSITIVE_INFINITY : init[i];
}
} else {
for (i = 0; i < n; i++)
soln[i] = soln2[i] = target.get(i) ? 0.0 : inf.get(i) ? Double.POSITIVE_INFINITY : 0.0;
}
// Determine set of states actually need to compute values for
unknown = new BitSet();
unknown.set(0, n);
unknown.andNot(target);
unknown.andNot(inf);
if (known != null) unknown.andNot(known);
// Start iterations
iters = 0;
done = false;
while (!done && iters < maxIters) {
// mainLog.println(soln);
iters++;
// Matrix-vector multiply and min/max ops
stpg.mvMultRewMinMax(soln, rewards, min1, min2, soln2, unknown, false, null);
// Check termination
done = PrismUtils.doublesAreClose(soln, soln2, termCritParam, termCrit == TermCrit.ABSOLUTE);
// Swap vectors for next iter
tmpsoln = soln;
soln = soln2;
soln2 = tmpsoln;
}
// Finished value iteration
timer = System.currentTimeMillis() - timer;
if (verbosity >= 1) {
mainLog.print("Value iteration (" + (min1 ? "min" : "max") + (min2 ? "min" : "max") + ")");
mainLog.println(" took " + iters + " iterations and " + timer / 1000.0 + " seconds.");
}
// Non-convergence is an error (usually)
if (!done && errorOnNonConverge) {
String msg = "Iterative method did not converge within " + iters + " iterations.";
msg +=
"\nConsider using a different numerical method or increasing the maximum number of iterations";
throw new PrismException(msg);
}
// Return results
res = new ModelCheckerResult();
res.soln = soln;
res.numIters = iters;
res.timeTaken = timer / 1000.0;
return res;
}
