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

Example 6 with ArithExpr

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

the class EncoderSlice method computeValidRange.

/*
   * Convert a set of ranges and a packet field to a symbolic boolean expression
   */
private BoolExpr computeValidRange(Set<SubRange> ranges, ArithExpr field) {
    BoolExpr acc = mkFalse();
    for (SubRange range : ranges) {
        int start = range.getStart();
        int end = range.getEnd();
        if (start == end) {
            BoolExpr val = mkEq(field, mkInt(start));
            acc = mkOr(acc, val);
        } else {
            BoolExpr val1 = mkGe(field, mkInt(start));
            BoolExpr val2 = mkLe(field, mkInt(end));
            acc = mkOr(acc, mkAnd(val1, val2));
        }
    }
    return (BoolExpr) acc.simplify();
}

Example 7 with ArithExpr

use of com.microsoft.z3.ArithExpr 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 8 with ArithExpr

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

the class PropertyAdder method recursiveReachability.

/*
   * Generates constraints for reachability through some neighbor.
   * If a router forwards to some neighbor with id label > 0, then the id of this router is
   * greater than that of all next hops. This prevents considering loops and also means that
   * we interpret the router as reachable. If there is no such neighbor, then this router is
   * not reachable and we set the id to 0.
   */
private BoolExpr recursiveReachability(Context ctx, EncoderSlice slice, List<GraphEdge> edges, Map<String, ArithExpr> idVars, String router, ArithExpr id) {
    ArithExpr zero = ctx.mkInt(0);
    BoolExpr hasRecursiveRoute = ctx.mkFalse();
    BoolExpr largerIds = ctx.mkTrue();
    for (GraphEdge edge : edges) {
        if (!edge.isAbstract()) {
            BoolExpr fwd = _encoderSlice.getForwardsAcross().get(router, edge);
            if (edge.getPeer() != null) {
                ArithExpr peerId = idVars.get(edge.getPeer());
                BoolExpr peerReachable = ctx.mkGt(peerId, zero);
                BoolExpr sendToReachable = ctx.mkAnd(fwd, peerReachable);
                hasRecursiveRoute = ctx.mkOr(hasRecursiveRoute, sendToReachable);
                BoolExpr increasingId = ctx.mkImplies(sendToReachable, ctx.mkGt(id, peerId));
                largerIds = ctx.mkAnd(largerIds, increasingId);
            }
        }
    }
    return slice.mkIf(hasRecursiveRoute, largerIds, ctx.mkEq(id, zero));
}

Example 9 with ArithExpr

use of com.microsoft.z3.ArithExpr 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 10 with ArithExpr

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

the class PropertyChecker method relateFailures.

private BoolExpr relateFailures(Encoder enc1, Encoder enc2) {
    BoolExpr related = enc1.mkTrue();
    for (GraphEdge ge : enc1.getMainSlice().getGraph().getAllRealEdges()) {
        ArithExpr a1 = enc1.getSymbolicFailures().getFailedVariable(ge);
        ArithExpr a2 = enc2.getSymbolicFailures().getFailedVariable(ge);
        assert a1 != null;
        assert a2 != null;
        related = enc1.mkEq(a1, a2);
    }
    return related;
}