/**
* Compute invariants of a graph g by mining invariants from the transitive closure using {@code
* extractInvariantsUsingTC}, which returns an over-approximation of the invariants that hold
* (i.e. it may return invariants that do not hold, but may not fail to return an invariant that
* does not hold)
*
* @param g the graph of nodes of type LogEvent
* @param mineConcurrencyInvariants whether or not to also mine concurrency invariants
* @return the set of temporal invariants the graph satisfies
*/
public TemporalInvariantSet computeTransClosureInvariants(
TraceGraph<?> g, boolean mineConcurrencyInvariants) {
TimedTask mineInvariants = PerformanceMetrics.createTask("mineInvariants", false);
Set<ITemporalInvariant> overapproximatedInvariantsSet;
AbstractMain main = AbstractMain.getInstance();
// Compute the over-approximated set of invariants for the input graph.
try {
TimedTask itc = PerformanceMetrics.createTask("invariants_transitive_closure", false);
// Compute the transitive closure.
AllRelationsTransitiveClosure transitiveClosure = new AllRelationsTransitiveClosure(g);
// Get the over-approximation.
itc.stop();
if (main.options.doBenchmarking) {
logger.info("BENCHM: " + itc);
}
TimedTask io = PerformanceMetrics.createTask("invariants_approximation", false);
// Extract invariants for all relations, iteratively. Since we are
// not considering invariants over multiple relations, this is
// sufficient.
overapproximatedInvariantsSet = new LinkedHashSet<ITemporalInvariant>();
for (String relation : g.getRelations()) {
overapproximatedInvariantsSet.addAll(
extractInvariantsFromTC(
g, transitiveClosure.get(relation), relation, mineConcurrencyInvariants));
}
io.stop();
if (main.options.doBenchmarking) {
logger.info("BENCHM: " + io);
}
// logger.info("Over-approx set: "
// + overapproximatedInvariantsSet.toString());
} finally {
mineInvariants.stop();
}
return new TemporalInvariantSet(overapproximatedInvariantsSet);
}
public AllRelationsTransitiveClosure(TraceGraph<?> g) {
for (String relation : g.getRelations()) {
tcs.put(relation, g.getTransitiveClosure(relation));
}
}
/**
* Extract an over-approximated set of invariants from the transitive closure {@code tc} of the
* graph {@code g}.
*
* @param g the graph over LogEvent
* @param tc the transitive closure (of {@code g}) from which to mine invariants
* @param relation the relation to consider for the invariants
* @return the over-approximated set of invariants
* @throws Exception
*/
private Set<ITemporalInvariant> extractInvariantsFromTC(
TraceGraph<?> g, TransitiveClosure tc, String relation, boolean mineConcurrencyInvariants) {
// This maintains the mapping from event type to a map of trace ids ->
// list of event instances in the trace. This is used to check
// reachability only between event instances that are in the same trace.
Map<EventType, Map<Integer, List<EventNode>>> etypeToTraceIdToENode =
new LinkedHashMap<EventType, Map<Integer, List<EventNode>>>();
// Initialize the partitions map: each unique label maps to a list of
// nodes with that label.
for (EventNode node : g.getNodes()) {
if (node.getEType().isSpecialEventType()) {
/**
* The inclusion of INITIAL and TERMINAL states in the graphs generates the following types
* of "tautological" invariants (for all event types X):
*
* <pre>
* - x AP TERMINAL
* - INITIAL AP x
* - x AP TERMINAL
* - x AFby TERMINAL
* - TERMINAL NFby INITIAL
* </pre>
*
* <p>NOTE: x AP TERMINAL is not actually a tautological invariant, but we do not
* mine/include it because we instead use x AFby INITIAL.
*
* <p>We filter these out by simply ignoring any temporal invariants of the form x INV y
* where x or y in {INITIAL, TERMINAL}. This is useful because it relieves us from
* checking/reporting invariants which are true for all graphs produced with typical
* construction.
*/
continue;
}
Map<Integer, List<EventNode>> map;
EventType etype = node.getEType();
if (!etypeToTraceIdToENode.containsKey(etype)) {
map = new LinkedHashMap<Integer, List<EventNode>>();
etypeToTraceIdToENode.put(etype, map);
} else {
map = etypeToTraceIdToENode.get(etype);
}
List<EventNode> list;
int tid = node.getTraceID();
if (!map.containsKey(tid)) {
list = new LinkedList<EventNode>();
map.put(tid, list);
} else {
list = map.get(tid);
}
list.add(node);
}
Set<ITemporalInvariant> pathInvs = new LinkedHashSet<ITemporalInvariant>();
Set<ITemporalInvariant> neverConcurInvs = new LinkedHashSet<ITemporalInvariant>();
Set<ITemporalInvariant> alwaysConcurInvs = new LinkedHashSet<ITemporalInvariant>();
Set<Pair<EventType, EventType>> observedPairs = new LinkedHashSet<Pair<EventType, EventType>>();
int numTraces = g.getNumTraces();
for (Entry<EventType, Map<Integer, List<EventNode>>> e1Entry :
etypeToTraceIdToENode.entrySet()) {
EventType e1 = e1Entry.getKey();
// ///////////////// Determine if "INITIAL AFby e1" is true
// Check if an e1 node appeared in every trace, if yes then inv
// true.
if (e1Entry.getValue().keySet().size() == numTraces) {
pathInvs.add(
new AlwaysFollowedInvariant(
StringEventType.newInitialStringEventType(), e1, Event.defTimeRelationStr));
}
// /////////////////
for (Entry<EventType, Map<Integer, List<EventNode>>> e2Entry :
etypeToTraceIdToENode.entrySet()) {
EventType e2 = e2Entry.getKey();
// If we have done (e1,e2) then do not do (e2,e1) because for
// pair (e1,e2) we derive orderings and invariants for both
// (e1,e2) and (e2,e1) -- this is done so that we can do correct
// subsumption of invariants (and concurrency invariants require
// symmetrical information).
if (observedPairs.contains(new Pair<EventType, EventType>(e2, e1))) {
continue;
}
observedPairs.add(new Pair<EventType, EventType>(e1, e2));
// ///////////////////////////////
// Derive the ordering summary between each instance of e1 and
// every instance of e2.
EventOrderingSummary E1orderE2 =
summarizeOrderings(e1Entry.getValue(), e2Entry.getValue(), tc);
// Do same for e2,e1.
EventOrderingSummary E2orderE1 =
summarizeOrderings(e2Entry.getValue(), e1Entry.getValue(), tc);
// ///////////////////////////////
// Whether or not never ordered invariant was added --
// determines whether or not NFby invariants are added
// below.
boolean addedNeverOrdered = false;
if (mineConcurrencyInvariants) {
// Ignore local versions of alwaysOrdered and
// neverOrdered since they are trivially true and false
// respectively.
if (!((DistEventType) e1)
.getProcessName()
.equals(((DistEventType) e2).getProcessName())) {
// Because lack of order is symmetric, it doesn't matter
// if we use E1orderE2.neverOrdered or
// E2orderE1.neverOrdered.
if (E1orderE2.neverOrdered) {
alwaysConcurInvs.add(
new AlwaysConcurrentInvariant((DistEventType) e2, (DistEventType) e1, relation));
addedNeverOrdered = true;
}
// Because complete order is symmetric, it doesn't
// matter if we use E1orderE2.alwaysOrdered or
// E2orderE1.alwaysOrdered.
if (E1orderE2.alwaysOrdered
&& !E1orderE2.alwaysPrecedes
&& !E1orderE2.alwaysFollowedBy
&& !E2orderE1.alwaysPrecedes
&& !E2orderE1.alwaysFollowedBy) {
neverConcurInvs.add(
new NeverConcurrentInvariant((DistEventType) e2, (DistEventType) e1, relation));
}
}
}
if (!addedNeverOrdered) {
// Note that ACWith subsumes NFby, which is why we add NFby
// if not(ACWith).
if (E1orderE2.neverFollowedBy) {
pathInvs.add(new NeverFollowedInvariant(e1, e2, relation));
}
if (E2orderE1.neverFollowedBy) {
pathInvs.add(new NeverFollowedInvariant(e2, e1, relation));
}
}
if (E1orderE2.alwaysFollowedBy) {
pathInvs.add(new AlwaysFollowedInvariant(e1, e2, relation));
}
if (E2orderE1.alwaysFollowedBy) {
pathInvs.add(new AlwaysFollowedInvariant(e2, e1, relation));
}
if (E1orderE2.alwaysPrecedes) {
pathInvs.add(new AlwaysPrecedesInvariant(e2, e1, relation));
}
if (E2orderE1.alwaysPrecedes) {
pathInvs.add(new AlwaysPrecedesInvariant(e1, e2, relation));
}
}
}
// Merge the concurrency and path invariant sets.
pathInvs.addAll(neverConcurInvs);
pathInvs.addAll(alwaysConcurInvs);
return pathInvs;
}
