analysis

Class NFAAnalysisTools

java.lang.Object

analysis.NFAAnalysisTools

public class NFAAnalysisTools
extends Object

Constructor Summary

Constructors

Constructor and Description
NFAAnalysisTools()

Method Summary

Modifier and Type	Method and Description
static NFAGraph	complementDfa(NFAGraph dfa)
static NFAGraph	convertUpNFAToNFAGraph(NFAGraph m, HashMap<NFAVertexND,UPNFAState> newStateMap)
static NFAGraph	createFilter() Creates an NFA graph representing the Mohri filter.
static NFAGraph	determinize(NFAGraph input, Set<NFAVertexND> reachableFromStart, Set<TransitionLabel> alphabet)
static NFAGraph	dfaIntersection(NFAGraph m1, NFAGraph m2)
static Set<TransitionLabel>	getAlphabet(NFAGraph n)
static LinkedList<NFAGraph>	getEpsilonStronglyConnectedComponents(NFAGraph m) Constructs a list of NFA graphs each representing a strongly connected component containing only epsilon transitions in the graph given as parameter.
static LinkedList<NFAGraph>	getStronglyConnectedComponents(NFAGraph m) Constructs a list of NFA graphs each representing a strongly connected component in the graph given as parameter.
protected static boolean	isInterrupted()
static NFAGraph	makeTrim(NFAGraph m) Removes all useless states from an NFA graph.
static NFAGraph	makeTrimAlternative(NFAGraph m) Removes all useless states from an NFA graph.
static NFAGraph	makeTrimFromStart(NFAGraph m)
static NFAGraph	makeTrimUPNFA(NFAGraph m, NFAGraph upnfa)
static Map<NFAVertexND,NFAGraph>	mergeStronglyConnectedComponents(NFAGraph m, boolean epsilon) Creates a single state for each strongly connected component.
static HashMap<NFAVertexND,Integer>	numWalksFrom(NFAGraph m, NFAVertexND s) Determines the number of walks between a vertex and all other vertices in a given graph.
static void	prepareForFilter(NFAGraph m, String modifyLabel, String selfloopLabel) Modifies an NFA graph so that it can be used with the Mohri filter.
static NFAGraph	productConstruction(NFAGraph m1, NFAGraph m2, HashMap<NFAEdge,TransitionLabel> originalWords)
static NFAGraph	productConstructionAFA(NFAGraph m) Calculates the product construction of a graph using the the Mohri filter.
static NFAGraph	productConstructionAFAFA(NFAGraph m)
static NFAGraph	productConstructionAFB(NFAGraph a, NFAGraph b)
static HashSet<NFAVertexND>	reachableWithEpsilon(NFAGraph n, NFAVertexND v)
static LinkedList<NFAEdge>	shortestPathBetween(NFAGraph m, NFAVertexND start, NFAVertexND finish)
static LinkedList<NFAEdge>	shortestPathTo(NFAGraph m, NFAVertexND finish) This function finds the shortest path from the initial state in the NFA to a certain finish state.
static HashMap<NFAVertexND,Integer>	topologicalSort(NFAGraph originalM) A function that uses Kahn's algorithm to find the topological order of the vertices in the graph.
static boolean	upNFAStateIsUseful(NFAGraph m, NFAGraph upnfa, UPNFAState upNFAState)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

NFAAnalysisTools

public NFAAnalysisTools()

Method Detail

prepareForFilter

public static void prepareForFilter(NFAGraph m,
                                    String modifyLabel,
                                    String selfloopLabel)

Modifies an NFA graph so that it can be used with the Mohri filter.

Parameters:

m - The NFA graph to modify

modifyLabel - The label to assign to the current epsilon transitions.

selfloopLabel - The label to assign to the selfloops added to all states.

createFilter

public static NFAGraph createFilter()

Creates an NFA graph representing the Mohri filter.

Returns:

the NFA graph

productConstructionAFB

public static NFAGraph productConstructionAFB(NFAGraph a,
                                              NFAGraph b)
                                       throws InterruptedException

Throws:

InterruptedException

productConstructionAFA

public static NFAGraph productConstructionAFA(NFAGraph m)
                                       throws InterruptedException

Calculates the product construction of a graph using the the Mohri filter.

Parameters:

m - The NFA to get the product construction of.

Returns:

The NFA representing the product construction.

Throws:

InterruptedException

productConstructionAFAFA

public static NFAGraph productConstructionAFAFA(NFAGraph m)
                                         throws InterruptedException

Throws:

InterruptedException

productConstruction

public static NFAGraph productConstruction(NFAGraph m1,
                                           NFAGraph m2,
                                           HashMap<NFAEdge,TransitionLabel> originalWords)
                                    throws InterruptedException

Throws:

InterruptedException

makeTrimFromStart

public static NFAGraph makeTrimFromStart(NFAGraph m)
                                  throws InterruptedException

Throws:

InterruptedException

makeTrimAlternative

public static NFAGraph makeTrimAlternative(NFAGraph m)
                                    throws InterruptedException

Removes all useless states from an NFA graph. This is done recursively by determining whether each vertex is connected to a useful vertex, recursively.

Parameters:

m - The NFA graph to remove all useless states from.

Returns:

The trimmed graph.

Throws:

InterruptedException

makeTrimUPNFA

public static NFAGraph makeTrimUPNFA(NFAGraph m,
                                     NFAGraph upnfa)
                              throws InterruptedException

Throws:

InterruptedException

upNFAStateIsUseful

public static boolean upNFAStateIsUseful(NFAGraph m,
                                         NFAGraph upnfa,
                                         UPNFAState upNFAState)
                                  throws InterruptedException

Throws:

InterruptedException

complementDfa

public static NFAGraph complementDfa(NFAGraph dfa)

makeTrim

public static NFAGraph makeTrim(NFAGraph m)
                         throws InterruptedException

Removes all useless states from an NFA graph. This is done by reversing the graph and determining which states are reachable from the final state. Typically this method was found to be slower than the other makeTrim method.

Parameters:

m - The NFA graph to remove all useless states from.

Returns:

The trimmed graph.

Throws:

InterruptedException

convertUpNFAToNFAGraph

public static NFAGraph convertUpNFAToNFAGraph(NFAGraph m,
                                              HashMap<NFAVertexND,UPNFAState> newStateMap)

getStronglyConnectedComponents

public static LinkedList<NFAGraph> getStronglyConnectedComponents(NFAGraph m)
                                                           throws InterruptedException

Constructs a list of NFA graphs each representing a strongly connected component in the graph given as parameter.

Parameters:

m - The NFA graph to find the strongly connected components in.

Returns:

A list containing all the strongly connected components.

Throws:

InterruptedException

getEpsilonStronglyConnectedComponents

public static LinkedList<NFAGraph> getEpsilonStronglyConnectedComponents(NFAGraph m)
                                                                  throws InterruptedException

Constructs a list of NFA graphs each representing a strongly connected component containing only epsilon transitions in the graph given as parameter.

Parameters:

m - The NFA graph to find the strongly connected components in.

Returns:

A list containing all the strongly connected components, with only epsilon transitions between the states.

Throws:

InterruptedException

mergeStronglyConnectedComponents

public static Map<NFAVertexND,NFAGraph> mergeStronglyConnectedComponents(NFAGraph m,
                                                                         boolean epsilon)
                                                                  throws InterruptedException

Creates a single state for each strongly connected component.

Parameters:

m - The NFA graph to merge the epsilon strongly connected components in.

epsilon - True if only epsilon strongly connected components should be merged, false if all strongly connected components should be merged.

Returns:

A HashMap containing the merged states as key and the original escc as value.

Throws:

InterruptedException

numWalksFrom

public static HashMap<NFAVertexND,Integer> numWalksFrom(NFAGraph m,
                                                        NFAVertexND s)

Determines the number of walks between a vertex and all other vertices in a given graph.

Parameters:

m - The graph to count the walks in.

s - The starting vertex.

Returns:

A HashMap containing every destination vertex as key and the number of walks to this vertex as value.

getAlphabet

public static Set<TransitionLabel> getAlphabet(NFAGraph n)

shortestPathTo

public static LinkedList<NFAEdge> shortestPathTo(NFAGraph m,
                                                 NFAVertexND finish)

This function finds the shortest path from the initial state in the NFA to a certain finish state.

Parameters:

m - The graph representing the NFA.

finish - The state to search to.

Returns:

A linked list containing the edges in the path.

shortestPathBetween

public static LinkedList<NFAEdge> shortestPathBetween(NFAGraph m,
                                                      NFAVertexND start,
                                                      NFAVertexND finish)

reachableWithEpsilon

public static HashSet<NFAVertexND> reachableWithEpsilon(NFAGraph n,
                                                        NFAVertexND v)

determinize

public static NFAGraph determinize(NFAGraph input,
                                   Set<NFAVertexND> reachableFromStart,
                                   Set<TransitionLabel> alphabet)
                            throws InterruptedException

Throws:

InterruptedException

dfaIntersection

public static NFAGraph dfaIntersection(NFAGraph m1,
                                       NFAGraph m2)

topologicalSort

public static HashMap<NFAVertexND,Integer> topologicalSort(NFAGraph originalM)

A function that uses Kahn's algorithm to find the topological order of the vertices in the graph.

Parameters:

originalM - The NFA graph to find the topological order for.

Returns:

A map to find the position of each vertex in the topological order.

isInterrupted

protected static boolean isInterrupted()