8. The method of claim 3, wherein the match patterns correspond to a plurality of match-set nodes, the match-set nodes being formed into a match-set node graph of connected match-set nodes based on the query, starting with an empty accessibility graph, the generating accessibility graphs step comprising: matching match patterns corresponding to first match-set nodes of the match-set node graph with patterns of edges of each of the separated portions; adding to the accessibility graph a first matched match-set node if corresponding match patterns of the first match-set node is found and adding one first match node for each match connected below the first matched match-set node; matching match patterns corresponding to second match-set nodes that appear below the first matched match-set node in the match-set node graph, if a match is found for any of the second match-set nodes, then adding to the accessibility graph second matched match-set nodes connected below the first matched match-set node and for each match, adding one second match node connected below the second matched match-set node; and generating at least a data edge emanating from each of the match nodes labeled by at least one of a variable of a respective corresponding match pattern and an identification of a part of each of the separated portions identified by the respective corresponding match pattern.
8. The method of claim 3, wherein the match patterns correspond to a plurality of match-set nodes, the match-set nodes being formed into a match-set node graph of connected match-set nodes based on the query, starting with an empty accessibility graph, the generating accessibility graphs step comprising: matching match patterns corresponding to first match-set nodes of the match-set node graph with patterns of edges of each of the separated portions; adding to the accessibility graph a first matched match-set node if corresponding match patterns of the first match-set node is found and adding one first match node for each match connected below the first matched match-set node; matching match patterns corresponding to second match-set nodes that appear below the first matched match-set node in the match-set node graph, if a match is found for any of the second match-set nodes, then adding to the accessibility graph second matched match-set nodes connected below the first matched match-set node and for each match, adding one second match node connected below the second matched match-set node; and generating at least a data edge emanating from each of the match nodes labeled by at least one of a variable of a respective corresponding match pattern and an identification of a part of each of the separated portions identified by the respective corresponding match pattern. 9. The method of claim 8, further comprising: adding to the accessibility graph local existence nodes corresponding to each of the match-set nodes and match nodes and connecting the local existence nodes in a similar manner as the match-set nodes and the match nodes are connected; setting the values of each of the local existence nodes corresponding to leaf match nodes to ACC; setting values of each of the local existence nodes corresponding to other match nodes to ACC if values of the local existence nodes below each of the local existence nodes are all ACC; and setting values of each of the local existence nodes corresponding to match-set nodes to ACC if any values of local existence nodes below each of the local existence nodes is ACC.