This encoding is called the Caroline Word Graph (CWG).
- JohnPaul Adamovsky teaches how to construct a DAFSA hash function using a novel encoding with multiple integer arrays.- JohnPaul Adamovsky teaches how to construct a DAFSA using an array of integers.Wikimedia Commons has media related to Deterministic acyclic finite state automaton. Tresoldi, Tiago (2020), "DAFSA: a Python library for Deterministic Acyclic Finite State Automata", Journal of Open Source Software, 5 (46): 1986, doi: 10.21105/joss.01986 An open source Python implementation.Proceedings, 8th international conference (DLT 2004), Auckland, New Zealand, December 2004, Lecture Notes in Computer Science, 3340, Springer-Verlag, pp.
Epifanio, Chiara Mignosi, Filippo Shallit, Jeffrey Venturini, Ilaria (2004), "Sturmian graphs and a conjecture of Moser", in Calude, Cristian S.(1990), "On the significance of the directed acyclic word graph in cryptology", Advances in Cryptology - AUSCRYPT '90, Lecture Notes in Computer Science, 453, Springer-Verlag, pp. One of the early mentions of the data structure.
"Applications of finite automata representing large vocabularies". Dictionary of Algorithms and Data Structures.
However, a DAFSA can represent these same four words using only six vertices v i for 0 ≤ i ≤ 5, and the following edges: an edge from v 0 to v 1 labeled "t", two edges from v 1 to v 2 labeled "a" and "o", an edge from v 2 to v 3 labeled "p", an edge v 3 to v 4 labeled "s", and edges from v 3 and v 4 to v 5 labeled with the end-of-string marker. A trie for those four words would have 12 vertices, one for each of the strings formed as a prefix of one of these words, or for one of the words followed by the end-of-string marker. Consider, for example, the four English words "tap", "taps", "top", and "tops". Comparison to triesīy allowing the same vertices to be reached by multiple paths, a DAFSA may use significantly fewer vertices than the strongly related trie data structure. In fact, a deterministic finite state automaton is acyclic if and only if it recognizes a finite set of strings. The strings represented by the DAFSA are formed by the symbols on paths in the graph from the source vertex to any sink vertex (a vertex with no outgoing edges). ContentsĪ DAFSA is a special case of a finite state recognizer that takes the form of a directed acyclic graph with a single source vertex (a vertex with no incoming edges), in which each edge of the graph is labeled by a letter or symbol, and in which each vertex has at most one outgoing edge for each possible letter or symbol.
Algorithms exist to construct and maintain such automata, while keeping them minimal. In computer science, a deterministic acyclic finite state automaton ( DAFSA), also called a directed acyclic word graph ( DAWG though that name also refers to a related data structure that functions as a suffix index ) is a data structure that represents a set of strings, and allows for a query operation that tests whether a given string belongs to the set in time proportional to its length. WikiMili Deterministic acyclic finite state automaton Last updated MaThe strings "tap", "taps", "top", and "tops" stored in a trie (left) and a DAFSA (right), EOW stands for End-of-word.