Examples with BitVecExpr com.microsoft.z3.BitVecExpr used on opensource projects

Example 1 with BitVecExpr

use of com.microsoft.z3.BitVecExpr in project batfish by batfish.

the class EncoderSlice method ipWildCardBound.

/*
   * Create a boolean expression for a variable being withing an IpWildCard bound
   */
private BoolExpr ipWildCardBound(BitVecExpr field, IpWildcard wc) {
    BitVecExpr ip = getCtx().mkBV(wc.getIp().asLong(), 32);
    BitVecExpr mask = getCtx().mkBV(~wc.getWildcard().asLong(), 32);
    return mkEq(getCtx().mkBVAND(field, mask), getCtx().mkBVAND(ip, mask));
}

Example 2 with BitVecExpr

use of com.microsoft.z3.BitVecExpr in project batfish by batfish.

the class PropertyAdder method instrumentPathLength.

// Potentially useful in the future to optimize reachability when we know
// that there can't be routing loops e.g., due to a preliminary static analysis
/* public Map<String, BoolExpr> instrumentReachabilityFast(String router) {
    Context ctx = _encoderSlice.getCtx();
    Solver solver = _encoderSlice.getSolver();
    Map<String, BoolExpr> reachableVars = new HashMap<>();
    String sliceName = _encoderSlice.getSliceName();
    _encoderSlice
        .getGraph()
        .getConfigurations()
        .forEach(
            (r, conf) -> {
              int id = _encoderSlice.getEncoder().getId();
              String s2 = id + "_" + sliceName + "_reachable_" + r;
              BoolExpr var = ctx.mkBoolConst(s2);
              reachableVars.put(r, var);
              _encoderSlice.getAllVariables().put(var.toString(), var);
            });

    BoolExpr baseReach = reachableVars.get(router);
    _encoderSlice.add(baseReach);
    _encoderSlice
        .getGraph()
        .getEdgeMap()
        .forEach(
            (r, edges) -> {
              if (!r.equals(router)) {
                BoolExpr reach = reachableVars.get(r);
                BoolExpr hasRecursiveRoute = ctx.mkFalse();
                for (GraphEdge edge : edges) {
                  if (!edge.isAbstract()) {
                    BoolExpr fwd = _encoderSlice.getForwardsAcross().get(r, edge);
                    if (edge.getPeer() != null) {
                      BoolExpr peerReachable = reachableVars.get(edge.getPeer());
                      BoolExpr sendToReachable = ctx.mkAnd(fwd, peerReachable);
                      hasRecursiveRoute = ctx.mkOr(hasRecursiveRoute, sendToReachable);
                    }
                  }
                }
                solver.add(ctx.mkEq(reach, hasRecursiveRoute));
              }
            });

    return reachableVars;
  }

  public Map<String, BoolExpr> instrumentReachabilityFast(Set<GraphEdge> ges) {
    Context ctx = _encoderSlice.getCtx();
    Solver solver = _encoderSlice.getSolver();
    EncoderSlice slice = _encoderSlice;
    String sliceName = _encoderSlice.getSliceName();
    Graph g = slice.getGraph();
    Map<String, BoolExpr> reachableVars = new HashMap<>();

    _encoderSlice
        .getGraph()
        .getConfigurations()
        .forEach(
            (r, conf) -> {
              int id = _encoderSlice.getEncoder().getId();
              String s2 = id + "_" + sliceName + "_reachable_" + r;
              BoolExpr var = ctx.mkBoolConst(s2);
              reachableVars.put(r, var);
              _encoderSlice.getAllVariables().put(var.toString(), var);
            });

    for (Entry<String, List<GraphEdge>> entry : g.getEdgeMap().entrySet()) {
      String router = entry.getKey();
      List<GraphEdge> edges = entry.getValue();
      BoolExpr reach = reachableVars.get(router);

      // Add the base case, reachable if we forward to a directly connected interface
      BoolExpr hasDirectRoute = ctx.mkFalse();
      BoolExpr isAbsorbed = ctx.mkFalse();
      SymbolicRoute r = _encoderSlice.getBestNeighborPerProtocol(router, Protocol.CONNECTED);

      for (GraphEdge ge : edges) {
        if (!ge.isAbstract() && ges.contains(ge)) {
          // If a host, consider reachable
          if (g.isHost(router)) {
            hasDirectRoute = ctx.mkTrue();
            break;
          }
          // Reachable if we leave the network
          if (ge.getPeer() == null) {
            BoolExpr fwdIface = _encoderSlice.getForwardsAcross().get(ge.getRouter(), ge);
            assert (fwdIface != null);
            hasDirectRoute = ctx.mkOr(hasDirectRoute, fwdIface);
          }
          // Also reachable if connected route and we use it despite not forwarding
          if (r != null) {
            BitVecExpr dstIp = _encoderSlice.getSymbolicPacket().getDstIp();
            BitVecExpr ip = ctx.mkBV(ge.getStart().getIp().getIp().asLong(), 32);
            BoolExpr reachable = ctx.mkAnd(r.getPermitted(), ctx.mkEq(dstIp, ip));
            isAbsorbed = ctx.mkOr(isAbsorbed, reachable);
          }
        }
      }

      // Add the recursive case, where it is reachable through a neighbor
      BoolExpr hasRecursiveRoute = ctx.mkFalse();
      for (GraphEdge edge : edges) {
        if (!edge.isAbstract()) {
          BoolExpr fwd = _encoderSlice.getForwardsAcross().get(router, edge);
          if (edge.getPeer() != null) {
            BoolExpr peerReachable = reachableVars.get(edge.getPeer());
            BoolExpr sendToReachable = ctx.mkAnd(fwd, peerReachable);
            hasRecursiveRoute = ctx.mkOr(hasRecursiveRoute, sendToReachable);
          }
        }
      }

      BoolExpr cond = slice.mkOr(hasDirectRoute, isAbsorbed, hasRecursiveRoute);
      solver.add(slice.mkEq(reach, cond));
    }

    return reachableVars;
  } */
/*
   * Instruments the network with path length information to a
   * destination port corresponding to a graph edge ge.
   * A router has a path of length n if some neighbor has a path
   * with length n-1.
   */
Map<String, ArithExpr> instrumentPathLength(Set<GraphEdge> ges) {
    Context ctx = _encoderSlice.getCtx();
    Solver solver = _encoderSlice.getSolver();
    String sliceName = _encoderSlice.getSliceName();
    // Initialize path length variables
    Graph graph = _encoderSlice.getGraph();
    Map<String, ArithExpr> lenVars = new HashMap<>();
    for (String router : graph.getRouters()) {
        String name = _encoderSlice.getEncoder().getId() + "_" + sliceName + "_path-length_" + router;
        ArithExpr var = ctx.mkIntConst(name);
        lenVars.put(router, var);
        _encoderSlice.getAllVariables().put(var.toString(), var);
    }
    ArithExpr zero = ctx.mkInt(0);
    ArithExpr one = ctx.mkInt(1);
    ArithExpr minusOne = ctx.mkInt(-1);
    // Lower bound for all lengths
    lenVars.forEach((name, var) -> solver.add(ctx.mkGe(var, minusOne)));
    for (Entry<String, List<GraphEdge>> entry : graph.getEdgeMap().entrySet()) {
        String router = entry.getKey();
        List<GraphEdge> edges = entry.getValue();
        ArithExpr length = lenVars.get(router);
        // If there is a direct route, then we have length 0
        BoolExpr hasDirectRoute = ctx.mkFalse();
        BoolExpr isAbsorbed = ctx.mkFalse();
        SymbolicRoute r = _encoderSlice.getBestNeighborPerProtocol(router, Protocol.CONNECTED);
        for (GraphEdge ge : edges) {
            if (!ge.isAbstract() && ges.contains(ge)) {
                // Reachable if we leave the network
                if (ge.getPeer() == null) {
                    BoolExpr fwdIface = _encoderSlice.getForwardsAcross().get(ge.getRouter(), ge);
                    assert (fwdIface != null);
                    hasDirectRoute = ctx.mkOr(hasDirectRoute, fwdIface);
                }
                // Also reachable if connected route and we use it despite not forwarding
                if (r != null) {
                    BitVecExpr dstIp = _encoderSlice.getSymbolicPacket().getDstIp();
                    BitVecExpr ip = ctx.mkBV(ge.getStart().getAddress().getIp().asLong(), 32);
                    BoolExpr reach = ctx.mkAnd(r.getPermitted(), ctx.mkEq(dstIp, ip));
                    isAbsorbed = ctx.mkOr(isAbsorbed, reach);
                }
            }
        }
        // Otherwise, we find length recursively
        BoolExpr accNone = ctx.mkTrue();
        BoolExpr accSome = ctx.mkFalse();
        for (GraphEdge edge : edges) {
            if (!edge.isAbstract() && edge.getPeer() != null) {
                BoolExpr dataFwd = _encoderSlice.getForwardsAcross().get(router, edge);
                assert (dataFwd != null);
                ArithExpr peerLen = lenVars.get(edge.getPeer());
                accNone = ctx.mkAnd(accNone, ctx.mkOr(ctx.mkLt(peerLen, zero), ctx.mkNot(dataFwd)));
                ArithExpr newVal = ctx.mkAdd(peerLen, one);
                BoolExpr fwd = ctx.mkAnd(ctx.mkGe(peerLen, zero), dataFwd, ctx.mkEq(length, newVal));
                accSome = ctx.mkOr(accSome, fwd);
            }
        }
        BoolExpr guard = _encoderSlice.mkOr(hasDirectRoute, isAbsorbed);
        BoolExpr cond1 = _encoderSlice.mkIf(accNone, ctx.mkEq(length, minusOne), accSome);
        BoolExpr cond2 = _encoderSlice.mkIf(guard, ctx.mkEq(length, zero), cond1);
        solver.add(cond2);
    }
    return lenVars;
}

Example 3 with BitVecExpr

use of com.microsoft.z3.BitVecExpr in project batfish by batfish.

the class PropertyAdder method instrumentReachability.

/*
   * Add reachability information to the network for a destination edge.
   * Each router will have a boolean variable determining if it can reach
   * the destination. A router is reachable if it has some neighbor that
   * is also reachable.
   */
Map<String, BoolExpr> instrumentReachability(Set<GraphEdge> ges) {
    Context ctx = _encoderSlice.getCtx();
    Solver solver = _encoderSlice.getSolver();
    EncoderSlice slice = _encoderSlice;
    Map<String, BoolExpr> reachableVars = new HashMap<>();
    Map<String, ArithExpr> idVars = new HashMap<>();
    initializeReachabilityVars(slice, ctx, solver, reachableVars, idVars);
    Graph g = _encoderSlice.getGraph();
    for (Entry<String, List<GraphEdge>> entry : g.getEdgeMap().entrySet()) {
        String router = entry.getKey();
        List<GraphEdge> edges = entry.getValue();
        ArithExpr id = idVars.get(router);
        // Add the base case, reachable if we forward to a directly connected interface
        BoolExpr hasDirectRoute = ctx.mkFalse();
        BoolExpr isAbsorbed = ctx.mkFalse();
        SymbolicRoute r = _encoderSlice.getBestNeighborPerProtocol(router, Protocol.CONNECTED);
        for (GraphEdge ge : edges) {
            if (!ge.isAbstract() && ges.contains(ge)) {
                // If a host, consider reachable
                if (g.isHost(router)) {
                    hasDirectRoute = ctx.mkTrue();
                    break;
                }
                // Reachable if we leave the network
                if (ge.getPeer() == null) {
                    BoolExpr fwdIface = _encoderSlice.getForwardsAcross().get(ge.getRouter(), ge);
                    assert (fwdIface != null);
                    hasDirectRoute = ctx.mkOr(hasDirectRoute, fwdIface);
                }
                // Also reachable if connected route and we use it despite not forwarding
                if (r != null) {
                    BitVecExpr dstIp = _encoderSlice.getSymbolicPacket().getDstIp();
                    BitVecExpr ip = ctx.mkBV(ge.getStart().getAddress().getIp().asLong(), 32);
                    BoolExpr reach = ctx.mkAnd(r.getPermitted(), ctx.mkEq(dstIp, ip));
                    isAbsorbed = ctx.mkOr(isAbsorbed, reach);
                }
            }
        }
        // Add the recursive case, where it is reachable through a neighbor
        BoolExpr recursive = recursiveReachability(ctx, slice, edges, idVars, router, id);
        BoolExpr guard = ctx.mkOr(hasDirectRoute, isAbsorbed);
        BoolExpr cond = slice.mkIf(guard, ctx.mkEq(id, ctx.mkInt(1)), recursive);
        solver.add(cond);
    }
    return reachableVars;
}

Example 4 with BitVecExpr

use of com.microsoft.z3.BitVecExpr in project batfish by batfish.

the class TransferSSA method joinPoint.

/*
   * The [phi] function from SSA that merges variables that may differ across
   * different branches of an mkIf statement.
   */
private Pair<Expr, Expr> joinPoint(TransferParam<SymbolicRoute> p, TransferResult<BoolExpr, BoolExpr> r, BoolExpr guard, Pair<String, Pair<Expr, Expr>> values) {
    String variableName = values.getFirst();
    Expr trueBranch = values.getSecond().getFirst();
    Expr falseBranch = values.getSecond().getSecond();
    if (variableName.equals("RETURN") || variableName.equals("FALLTHROUGH")) {
        Expr t = (trueBranch == null ? _enc.mkFalse() : // can use False because the value has not been assigned
        trueBranch);
        Expr f = (falseBranch == null ? _enc.mkFalse() : falseBranch);
        Expr tass = (trueBranch == null ? r.getReturnAssignedValue() : _enc.mkTrue());
        Expr fass = (falseBranch == null ? r.getReturnAssignedValue() : _enc.mkTrue());
        BoolExpr newAss = _enc.mkIf(guard, (BoolExpr) tass, (BoolExpr) fass);
        BoolExpr retAss = createBoolVariableWith(p, "ASSIGNED", newAss);
        BoolExpr variable = (variableName.equals("RETURN") ? r.getReturnValue() : r.getFallthroughValue());
        BoolExpr newValue = _enc.mkIf(r.getReturnAssignedValue(), variable, _enc.mkIf(guard, (BoolExpr) t, (BoolExpr) f));
        BoolExpr ret = createBoolVariableWith(p, variableName, newValue);
        return new Pair<>(ret, retAss);
    }
    if (variableName.equals("PREFIX-LEN")) {
        Expr t = (trueBranch == null ? p.getData().getPrefixLength() : trueBranch);
        Expr f = (falseBranch == null ? p.getData().getPrefixLength() : falseBranch);
        ArithExpr newValue = _enc.mkIf(guard, (ArithExpr) t, (ArithExpr) f);
        newValue = _enc.mkIf(r.getReturnAssignedValue(), p.getData().getPrefixLength(), newValue);
        ArithExpr ret = createArithVariableWith(p, "PREFIX-LEN", newValue);
        p.getData().setPrefixLength(ret);
        return new Pair<>(ret, null);
    }
    if (variableName.equals("ADMIN-DIST")) {
        Expr t = (trueBranch == null ? p.getData().getAdminDist() : trueBranch);
        Expr f = (falseBranch == null ? p.getData().getAdminDist() : falseBranch);
        ArithExpr newValue = _enc.mkIf(guard, (ArithExpr) t, (ArithExpr) f);
        newValue = _enc.mkIf(r.getReturnAssignedValue(), p.getData().getAdminDist(), newValue);
        ArithExpr ret = createArithVariableWith(p, "ADMIN-DIST", newValue);
        p.getData().setAdminDist(ret);
        return new Pair<>(ret, null);
    }
    if (variableName.equals("LOCAL-PREF")) {
        Expr t = (trueBranch == null ? p.getData().getLocalPref() : trueBranch);
        Expr f = (falseBranch == null ? p.getData().getLocalPref() : falseBranch);
        ArithExpr newValue = _enc.mkIf(guard, (ArithExpr) t, (ArithExpr) f);
        newValue = _enc.mkIf(r.getReturnAssignedValue(), p.getData().getLocalPref(), newValue);
        ArithExpr ret = createArithVariableWith(p, "LOCAL-PREF", newValue);
        p.getData().setLocalPref(ret);
        return new Pair<>(ret, null);
    }
    if (variableName.equals("METRIC")) {
        Expr t = (trueBranch == null ? p.getData().getMetric() : trueBranch);
        Expr f = (falseBranch == null ? p.getData().getMetric() : falseBranch);
        ArithExpr newValue = _enc.mkIf(guard, (ArithExpr) t, (ArithExpr) f);
        newValue = _enc.mkIf(r.getReturnAssignedValue(), p.getData().getMetric(), newValue);
        ArithExpr ret = createArithVariableWith(p, "METRIC", newValue);
        p.getData().setMetric(ret);
        return new Pair<>(ret, null);
    }
    if (variableName.equals("OSPF-TYPE")) {
        Expr t = (trueBranch == null ? p.getData().getOspfType().getBitVec() : trueBranch);
        Expr f = (falseBranch == null ? p.getData().getOspfType().getBitVec() : falseBranch);
        BitVecExpr newValue = _enc.mkIf(guard, (BitVecExpr) t, (BitVecExpr) f);
        newValue = _enc.mkIf(r.getReturnAssignedValue(), p.getData().getOspfType().getBitVec(), newValue);
        BitVecExpr ret = createBitVecVariableWith(p, "OSPF-TYPE", 2, newValue);
        p.getData().getOspfType().setBitVec(ret);
        return new Pair<>(ret, null);
    }
    for (Map.Entry<CommunityVar, BoolExpr> entry : p.getData().getCommunities().entrySet()) {
        CommunityVar cvar = entry.getKey();
        if (variableName.equals(cvar.getValue())) {
            Expr t = (trueBranch == null ? p.getData().getCommunities().get(cvar) : trueBranch);
            Expr f = (falseBranch == null ? p.getData().getCommunities().get(cvar) : falseBranch);
            BoolExpr newValue = _enc.mkIf(guard, (BoolExpr) t, (BoolExpr) f);
            newValue = _enc.mkIf(r.getReturnAssignedValue(), p.getData().getCommunities().get(cvar), newValue);
            BoolExpr ret = createBoolVariableWith(p, cvar.getValue(), newValue);
            p.getData().getCommunities().put(cvar, ret);
            return new Pair<>(ret, null);
        }
    }
    throw new BatfishException("[joinPoint]: unhandled case for " + variableName);
}

Example 5 with BitVecExpr

use of com.microsoft.z3.BitVecExpr in project batfish by batfish.

the class NodJob method computeSmtInput.

@Override
protected SmtInput computeSmtInput(long startTime, Context ctx) {
    NodProgram program = getNodProgram(ctx);
    BoolExpr expr = computeSmtConstraintsViaNod(program, _querySynthesizer.getNegate());
    Map<String, BitVecExpr> variablesAsConsts = program.getNodContext().getVariablesAsConsts();
    return new SmtInput(expr, variablesAsConsts);
}