prism-accumulation/prism/src/explicit/DTMCModelChecker.java

//==============================================================================
//	
//	Copyright (c) 2002-
//	Authors:
//	* Dave Parker <david.parker@comlab.ox.ac.uk> (University of Oxford)
//	
//------------------------------------------------------------------------------
//	
//	This file is part of PRISM.
//	
//	PRISM 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.
//	
//	PRISM 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 PRISM; if not, write to the Free Software Foundation,
//	Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
//	
//==============================================================================

package explicit;

import java.util.*;

import prism.*;
import explicit.StateValues;
import explicit.rewards.*;
import parser.ast.*;

/**
 * Explicit-state model checker for discrete-time Markov chains (DTMCs).
 */
public class DTMCModelChecker extends ProbModelChecker
{
	// Model checking functions

	/**
	 * Compute probabilities for the contents of a P operator.
	 */
	protected StateValues checkProbPathFormula(Model model, Expression expr) throws PrismException
	{
		// Test whether this is a simple path formula (i.e. PCTL)
		// and then pass control to appropriate method. 
		if (expr.isSimplePathFormula()) {
			return checkProbPathFormulaSimple(model, expr);
		} else {
			throw new PrismException("Explicit engine does not yet handle LTL-style path formulas");
		}
	}

	/**
	 * Compute probabilities for a simple, non-LTL path operator.
	 */
	protected StateValues checkProbPathFormulaSimple(Model model, Expression expr) throws PrismException
	{
		StateValues probs = null;

		// Temporal operators
		if (expr instanceof ExpressionTemporal) {
			ExpressionTemporal exprTemp = (ExpressionTemporal) expr;
			// Until
			if (exprTemp.getOperator() == ExpressionTemporal.P_U) {
				if (exprTemp.hasBounds()) {
					probs = checkProbBoundedUntil(model, exprTemp);
				} else {
					probs = checkProbUntil(model, exprTemp);
				}
			}
			// Anything else - convert to until and recurse
			else {
				probs = checkProbPathFormulaSimple(model, exprTemp.convertToUntilForm());
			}
		}

		if (probs == null)
			throw new PrismException("Unrecognised path operator in P operator");

		return probs;
	}

	/**
	 * Compute probabilities for a bounded until operator.
	 */
	protected StateValues checkProbBoundedUntil(Model model, ExpressionTemporal expr) throws PrismException
	{
		int time;
		BitSet b1, b2;
		StateValues probs = null;
		ModelCheckerResult res = null;

		// get info from bounded until
		time = expr.getUpperBound().evaluateInt(constantValues);
		if (expr.upperBoundIsStrict())
			time--;
		if (time < 0) {
			String bound = expr.upperBoundIsStrict() ? "<" + (time + 1) : "<=" + time;
			throw new PrismException("Invalid bound " + bound + " in bounded until formula");
		}

		// model check operands first
		b1 = (BitSet) checkExpression(model, expr.getOperand1());
		b2 = (BitSet) checkExpression(model, expr.getOperand2());

		// compute probabilities

		// a trivial case: "U<=0"
		if (time == 0) {
			// prob is 1 in b2 states, 0 otherwise
			probs = StateValues.createFromBitSetAsDoubles(model.getNumStates(), b2);
		} else {
			res = computeBoundedUntilProbs((DTMC) model, b1, b2, time);
			probs = StateValues.createFromDoubleArray(res.soln);
		}

		return probs;
	}

	/**
	 * Compute probabilities for an (unbounded) until operator.
	 */
	protected StateValues checkProbUntil(Model model, ExpressionTemporal expr) throws PrismException
	{
		BitSet b1, b2;
		StateValues probs = null;
		ModelCheckerResult res = null;

		// model check operands first
		b1 = (BitSet) checkExpression(model, expr.getOperand1());
		b2 = (BitSet) checkExpression(model, expr.getOperand2());

		// print out some info about num states
		// mainLog.print("\nb1 = " + JDD.GetNumMintermsString(b1,
		// allDDRowVars.n()));
		// mainLog.print(" states, b2 = " + JDD.GetNumMintermsString(b2,
		// allDDRowVars.n()) + " states\n");

		res = computeUntilProbs((DTMC) model, b1, b2);
		probs = StateValues.createFromDoubleArray(res.soln);

		return probs;
	}

	/**
	 * Compute rewards for the contents of an R operator.
	 */
	protected StateValues checkRewardFormula(Model model, MCRewards modelRewards, Expression expr) throws PrismException
	{
		StateValues rewards = null;
		
		if (expr instanceof ExpressionTemporal) {
			ExpressionTemporal exprTemp = (ExpressionTemporal) expr;
			switch (exprTemp.getOperator()) {
			case ExpressionTemporal.R_F:
				rewards = checkRewardReach(model, modelRewards, exprTemp);
				break;
			default:
				throw new PrismException("Explicit engine does not yet handle the " + exprTemp.getOperatorSymbol() + " operator in the R operator");
			}
		}
		
		if (rewards == null)
			throw new PrismException("Unrecognised operator in R operator");

		return rewards;
	}

	/**
	 * Compute rewards for a reachability reward operator.
	 */
	protected StateValues checkRewardReach(Model model, MCRewards modelRewards, ExpressionTemporal expr) throws PrismException
	{
		BitSet b;
		StateValues rewards = null;
		ModelCheckerResult res = null;

		// model check operand first
		b = (BitSet) checkExpression(model, expr.getOperand2());

		// print out some info about num states
		// mainLog.print("\nb = " + JDD.GetNumMintermsString(b1,
		// allDDRowVars.n()));

		res = computeReachRewards((DTMC) model, modelRewards, b);
		rewards = StateValues.createFromDoubleArray(res.soln);

		return rewards;
	}

	// Steady-state/transient probability computation

	/**
	 * Compute steady-state probability distribution (forwards).
	 * Optionally, use the passed in vector initDist as the initial probability distribution (time step 0).
	 * If null, start from initial state (or uniform distribution over multiple initial states).
	 * For reasons of efficiency, when a vector is passed in, it will be trampled over,
	 * so if you wanted it, take a copy. 
	 * @param dtmc The DTMC
	 * @param initDist Initial distribution (will be overwritten)
	 */
	public StateValues doSteadyState(DTMC dtmc, double initDist[]) throws PrismException
	{
		ModelCheckerResult res = null;
		int n;
		double initDistNew[] = null;
		StateValues probs = null;

		// TODO: BSCC computation
		
		// Store num states
		n = dtmc.getNumStates();

		// Build initial distribution (if not specified)
		if (initDist == null) {
			initDistNew = new double[n];
			for (int in : dtmc.getInitialStates()) {
				initDistNew[in] = 1 / dtmc.getNumInitialStates();
			}
		} else {
			initDistNew = initDist;
			throw new PrismException("Not implemented yet"); // TODO
		}

		// Compute transient probabilities
		res = computeSteadyStateProbs(dtmc, initDistNew);
		probs = StateValues.createFromDoubleArray(res.soln);

		return probs;
	}
	
	/**
	 * Compute transient probability distribution (forwards).
	 * Optionally, use the passed in vector initDist as the initial probability distribution (time step 0).
	 * If null, start from initial state (or uniform distribution over multiple initial states).
	 * For reasons of efficiency, when a vector is passed in, it will be trampled over,
	 * so if you wanted it, take a copy. 
	 * @param dtmc The DTMC
	 * @param k Time step
	 * @param initDist Initial distribution (will be overwritten)
	 */
	public StateValues doTransient(DTMC dtmc, int k, double initDist[]) throws PrismException
	{
		throw new PrismException("Not implemented yet");
	}
	
	// Numerical computation functions

	/**
	 * Compute reachability probabilities.
	 * i.e. compute the probability of reaching a state in {@code target}.
	 * @param dtmc The DTMC
	 * @param target Target states
	 */
	public ModelCheckerResult computeReachProbs(DTMC dtmc, BitSet target) throws PrismException
	{
		return computeReachProbs(dtmc, null, target, null, null);
	}

	/**
	 * Compute until probabilities.
	 * i.e. compute the probability of reaching a state in {@code target},
	 * while remaining in those in @{code remain}.
	 * @param dtmc The DTMC
	 * @param remain Remain in these states (optional: null means "all")
	 * @param target Target states
	 */
	public ModelCheckerResult computeUntilProbs(DTMC dtmc, BitSet remain, BitSet target) throws PrismException
	{
		return computeReachProbs(dtmc, remain, target, null, null);
	}

	/**
	 * 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 dtmc The DTMC
	 * @param remain Remain in these states (optional: null means "all")
	 * @param target Target states
	 * @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(DTMC dtmc, BitSet remain, BitSet target, double init[], BitSet known) throws PrismException
	{
		ModelCheckerResult res = null;
		BitSet no, yes;
		int i, n, numYes, numNo;
		long timer, timerProb0, timerProb1;

		// 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");
		}

		// Start probabilistic reachability
		timer = System.currentTimeMillis();
		mainLog.println("Starting probabilistic reachability...");

		// Check for deadlocks in non-target state (because breaks e.g. prob1)
		dtmc.checkForDeadlocks(target);

		// Store num states
		n = dtmc.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(dtmc, remain, target);
		} else {
			no = new BitSet();
		}
		timerProb0 = System.currentTimeMillis() - timerProb0;
		timerProb1 = System.currentTimeMillis();
		if (precomp && prob1) {
			yes = prob1(dtmc, remain, target);
		} else {
			yes = (BitSet) target.clone();
		}
		timerProb1 = System.currentTimeMillis() - timerProb1;

		// Print results of precomputation
		numYes = yes.cardinality();
		numNo = no.cardinality();
		mainLog.println("target=" + target.cardinality() + ", yes=" + numYes + ", no=" + numNo + ", maybe=" + (n - (numYes + numNo)));

		// Compute probabilities
		switch (solnMethod) {
		case VALUE_ITERATION:
			res = computeReachProbsValIter(dtmc, no, yes, init, known);
			break;
		case GAUSS_SEIDEL:
			res = computeReachProbsGaussSeidel(dtmc, no, yes, init, known);
			break;
		default:
			throw new PrismException("Unknown DTMC solution method " + solnMethod);
		}

		// Finished probabilistic reachability
		timer = System.currentTimeMillis() - timer;
		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;
	}

	/**
	 * Prob0 precomputation algorithm.
	 * i.e. determine the states of a DTMC which, with probability 0,
	 * reach a state in {@code target}, while remaining in those in @{code remain}.
	 * @param mdp The MDP
	 * @param remain Remain in these states (optional: null means "all")
	 * @param target Target states
	 */
	public BitSet prob0(DTMC dtmc, BitSet remain, BitSet target)
	{
		int n, iters;
		BitSet u, soln, unknown;
		boolean u_done;
		long timer;

		// Start precomputation
		timer = System.currentTimeMillis();
		mainLog.println("Starting Prob0...");

		// Special case: no target states
		if (target.cardinality() == 0) {
			soln = new BitSet(dtmc.getNumStates());
			soln.set(0, dtmc.getNumStates());
			return soln;
		}

		// Initialise vectors
		n = dtmc.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
			dtmc.prob0step(unknown, u, 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;
		mainLog.print("Prob0");
		mainLog.println(" took " + iters + " iterations and " + timer / 1000.0 + " seconds.");

		return u;
	}

	/**
	 * Prob1 precomputation algorithm.
	 * i.e. determine the states of a DTMC which, with probability 1,
	 * reach a state in {@code target}, while remaining in those in @{code remain}.
	 * @param mdp The MDP
	 * @param remain Remain in these states (optional: null means "all")
	 * @param target Target states
	 */
	public BitSet prob1(DTMC dtmc, BitSet remain, BitSet target)
	{
		int n, iters;
		BitSet u, v, soln, unknown;
		boolean u_done, v_done;
		long timer;

		// Start precomputation
		timer = System.currentTimeMillis();
		mainLog.println("Starting Prob1...");

		// Special case: no target states
		if (target.cardinality() == 0) {
			return new BitSet(dtmc.getNumStates());
		}

		// Initialise vectors
		n = dtmc.getNumStates();
		u = new BitSet(n);
		v = 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);

		// Nested fixed point loop
		iters = 0;
		u_done = false;
		// Greatest fixed point
		u.set(0, n);
		while (!u_done) {
			v_done = false;
			// Least fixed point - should start from 0 but we optimise by
			// starting from 'target', thus bypassing first iteration
			v.clear();
			v.or(target);
			soln.clear();
			soln.or(target);
			while (!v_done) {
				iters++;
				// Single step of Prob1
				dtmc.prob1step(unknown, u, v, soln);
				// Check termination (inner)
				v_done = soln.equals(v);
				// v = soln
				v.clear();
				v.or(soln);
			}
			// Check termination (outer)
			u_done = v.equals(u);
			// u = v
			u.clear();
			u.or(v);
		}

		// Finished precomputation
		timer = System.currentTimeMillis() - timer;
		mainLog.print("Prob1");
		mainLog.println(" took " + iters + " iterations and " + timer / 1000.0 + " seconds.");

		return u;
	}

	/**
	 * Compute reachability probabilities using value iteration.
	 * @param dtmc The DTMC
	 * @param no Probability 0 states
	 * @param yes Probability 1 states
	 * @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(DTMC dtmc, BitSet no, BitSet yes, double init[], BitSet known) throws PrismException
	{
		ModelCheckerResult res;
		BitSet unknown;
		int i, n, iters;
		double soln[], soln2[], tmpsoln[], initVal;
		boolean done;
		long timer;

		// Start value iteration
		timer = System.currentTimeMillis();
		mainLog.println("Starting value iteration...");

		// Store num states
		n = dtmc.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);

		// Start iterations
		iters = 0;
		done = false;
		while (!done && iters < maxIters) {
			iters++;
			// Matrix-vector multiply
			dtmc.mvMult(soln, soln2, unknown, false);
			// 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;
		mainLog.print("Value iteration");
		mainLog.println(" took " + iters + " iterations and " + timer / 1000.0 + " seconds.");

		// Return results
		res = new ModelCheckerResult();
		res.soln = soln;
		res.numIters = iters;
		res.timeTaken = timer / 1000.0;
		return res;
	}

	/**
	 * Compute reachability probabilities using Gauss-Seidel.
	 * @param dtmc The DTMC
	 * @param no Probability 0 states
	 * @param yes Probability 1 states
	 * @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(DTMC dtmc, BitSet no, BitSet yes, 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();
		mainLog.println("Starting Gauss-Seidel...");

		// Store num states
		n = dtmc.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
			maxDiff = dtmc.mvMultGS(soln, unknown, false, termCrit == TermCrit.ABSOLUTE);
			// Check termination
			done = maxDiff < termCritParam;
		}

		// Finished Gauss-Seidel
		timer = System.currentTimeMillis() - timer;
		mainLog.print("Gauss-Seidel");
		mainLog.println(" took " + iters + " iterations and " + timer / 1000.0 + " seconds.");

		// Return results
		res = new ModelCheckerResult();
		res.soln = soln;
		res.numIters = iters;
		res.timeTaken = timer / 1000.0;
		return res;
	}

	/**
	 * Compute bounded reachability probabilities.
	 * i.e. compute the probability of reaching a state in {@code target} within k steps.
	 * @param dtmc The DTMC
	 * @param target Target states
	 * @param k Bound
	 */
	public ModelCheckerResult computeBoundedReachProbs(DTMC dtmc, BitSet target, int k) throws PrismException
	{
		return computeBoundedReachProbs(dtmc, null, target, k, null, null);
	}

	/**
	 * Compute bounded until probabilities.
	 * i.e. compute the probability of reaching a state in {@code target},
	 * within k steps, and while remaining in states in @{code remain}.
	 * @param dtmc The DTMC
	 * @param remain Remain in these states (optional: null means "all")
	 * @param target Target states
	 * @param k Bound
	 */
	public ModelCheckerResult computeBoundedUntilProbs(DTMC dtmc, BitSet remain, BitSet target, int k) throws PrismException
	{
		return computeBoundedReachProbs(dtmc, remain, target, k, null, null);
	}

	/**
	 * Compute bounded reachability/until probabilities.
	 * i.e. compute the probability of reaching a state in {@code target},
	 * within k steps, and while remaining in states in @{code remain}.
	 * @param dtmc The DTMC
	 * @param remain Remain in these states (optional: null means "all")
	 * @param target Target states
	 * @param k Bound
	 * @param init Initial solution vector - pass null for default
	 * @param results Optional array of size b+1 to store (init state) results for each step (null if unused)
	 */
	public ModelCheckerResult computeBoundedReachProbs(DTMC dtmc, BitSet remain, BitSet target, int k, 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();
		mainLog.println("Starting bounded probabilistic reachability...");

		// Store num states
		n = dtmc.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) {
			// TODO: whether this is min or max should be specified somehow
			results[0] = Utils.minMaxOverArraySubset(soln2, dtmc.getInitialStates(), true);
		}

		// Start iterations
		iters = 0;
		while (iters < k) {

			iters++;
			// Matrix-vector multiply
			dtmc.mvMult(soln, soln2, target, true);
			// Store intermediate results if required
			// (compute min/max value over initial states for this step)
			if (results != null) {
				// TODO: whether this is min or max should be specified somehow
				results[iters] = Utils.minMaxOverArraySubset(soln2, dtmc.getInitialStates(), true);
			}
			// Swap vectors for next iter
			tmpsoln = soln;
			soln = soln2;
			soln2 = tmpsoln;
		}

		// Finished bounded probabilistic reachability
		timer = System.currentTimeMillis() - timer;
		mainLog.print("Bounded probabilistic reachability");
		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;
	}

	/**
	 * Compute expected reachability rewards.
	 * @param dtmc The DTMC
	 * @param mcRewards The rewards
	 * @param target Target states
	 */
	public ModelCheckerResult computeReachRewards(DTMC dtmc, MCRewards mcRewards, BitSet target) throws PrismException
	{
		return computeReachRewards(dtmc, mcRewards, target, null, null);
	}

	/**
	 * Compute expected reachability rewards.
	 * @param dtmc The DTMC
	 * @param mcRewards The rewards
	 * @param target Target states
	 * @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(DTMC dtmc, MCRewards mcRewards, BitSet target, 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();
		mainLog.println("Starting expected reachability...");

		// Check for deadlocks in non-target state (because breaks e.g. prob1)
		dtmc.checkForDeadlocks(target);

		// Store num states
		n = dtmc.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(dtmc, null, target);
		inf.flip(0, n);
		timerProb1 = System.currentTimeMillis() - timerProb1;

		// Print results of precomputation
		numTarget = target.cardinality();
		numInf = inf.cardinality();
		mainLog.println("target=" + numTarget + ", inf=" + numInf + ", rest=" + (n - (numTarget + numInf)));

		// Compute rewards
		switch (solnMethod) {
		case VALUE_ITERATION:
			res = computeReachRewardsValIter(dtmc, mcRewards, target, inf, init, known);
			break;
		default:
			throw new PrismException("Unknown DTMC solution method " + solnMethod);
		}

		// Finished expected reachability
		timer = System.currentTimeMillis() - timer;
		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 expected reachability rewards using value iteration.
	 * @param dtmc The DTMC
	 * @param mcRewards The rewards
	 * @param target Target states
	 * @param inf States for which reward is infinite
	 * @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(DTMC dtmc, MCRewards mcRewards, BitSet target, BitSet inf, 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();
		mainLog.println("Starting value iteration...");

		// Store num states
		n = dtmc.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
			dtmc.mvMultRew(soln, mcRewards, soln2, unknown, false);
			// 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;
		mainLog.print("Value iteration");
		mainLog.println(" took " + iters + " iterations and " + timer / 1000.0 + " seconds.");

		// Return results
		res = new ModelCheckerResult();
		res.soln = soln;
		res.numIters = iters;
		res.timeTaken = timer / 1000.0;
		return res;
	}

	/**
	 * Compute steady-state probabilities
	 * i.e. compute the long-run probability of being in each state,
	 * assuming the initial distribution {@code initDist}. 
	 * For space efficiency, the initial distribution vector will be modified and values over-written,  
	 * so if you wanted it, take a copy. 
	 * @param dtmc The DTMC
	 * @param initDist Initial distribution (will be overwritten)
	 */
	public ModelCheckerResult computeSteadyStateProbs(DTMC dtmc, double initDist[]) throws PrismException
	{
		ModelCheckerResult res;
		int n, iters;
		double soln[], soln2[], tmpsoln[];
		boolean done;
		long timer;

		// Start value iteration
		timer = System.currentTimeMillis();
		mainLog.println("Starting value iteration...");

		// Store num states
		n = dtmc.getNumStates();

		// Create solution vector(s)
		// For soln, we just use init (since we are free to modify this vector)
		soln = initDist;
		soln2 = new double[n];
		
		// No need to initialise solution vectors
		// (soln is done, soln2 will be immediately overwritten)

		// Start iterations
		iters = 0;
		done = false;
		while (!done && iters < maxIters) {
			iters++;
			// Matrix-vector multiply
			dtmc.vmMult(soln, soln2);
			// 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;
		mainLog.print("Value iteration");
		mainLog.println(" took " + iters + " iterations and " + timer / 1000.0 + " seconds.");

		// Return results
		res = new ModelCheckerResult();
		res.soln = soln;
		res.numIters = iters;
		res.timeTaken = timer / 1000.0;
		return res;
	}
	
	/**
	 * Compute transient probabilities
	 * i.e. compute the probability of being in each state at time step {@code k},
	 * assuming the initial distribution {@code initDist}. 
	 * For space efficiency, the initial distribution vector will be modified and values over-written,  
	 * so if you wanted it, take a copy. 
	 * @param dtmc The DTMC
	 * @param k Time step
	 * @param initDist Initial distribution (will be overwritten)
	 */
	public ModelCheckerResult computeTransientProbs(DTMC dtmc, int k, double initDist[]) throws PrismException
	{
		throw new PrismException("Not implemented yet");
	}
	
	/**
	 * Simple test program.
	 */
	public static void main(String args[])
	{
		DTMCModelChecker mc;
		DTMCSimple dtmc;
		ModelCheckerResult res;
		BitSet target;
		Map<String, BitSet> labels;
		try {
			mc = new DTMCModelChecker();
			dtmc = new DTMCSimple();
			dtmc.buildFromPrismExplicit(args[0]);
			//System.out.println(dtmc);
			labels = mc.loadLabelsFile(args[1]);
			//System.out.println(labels);
			target = labels.get(args[2]);
			if (target == null)
				throw new PrismException("Unknown label \"" + args[2] + "\"");
			for (int i = 3; i < args.length; i++) {
				if (args[i].equals("-nopre"))
					mc.setPrecomp(false);
			}
			res = mc.computeReachProbs(dtmc, target);
			System.out.println(res.soln[0]);
		} catch (PrismException e) {
			System.out.println(e);
		}
	}
}