On the Complexity of L-reachability.
Uloženo v:
| Název: | On the Complexity of L-reachability. |
|---|---|
| Autoři: | Komarath, Balagopal, Sarma, Jayalal, Sunil, K. S. |
| Zdroj: | Fundamenta Informaticae; 2016, Vol. 145 Issue 4, p471-483, 13p |
| Témata: | GEOMETRIC vertices, FOREIGN language education, GRAPH theory, COMPUTATIONAL complexity, PATH Pascal (Computer program language) |
| Abstrakt: | We initiate a complexity theoretic study of the language based graph reachability problem (L{REACH) : Fix a language L. Given a graph whose edges are labelled with alphabet symbols of the language L and two special vertices s and t, test if there is path P from s to t in the graph such that the concatenation of the symbols seen from s to t in the path P forms a string in the language L. We study variants of this problem with different graph classes and different language classes and obtain complexity theoretic characterizations for all of them. Our main results are the following:. Restricting the language using formal language theory we show that the complexity of L- REACH increases with the power of the formal language class. We show that there is a regular language for which the L{REACH is NL-complete even for undirected graphs. In the case of linear languages, the complexity of L{REACH does not go beyond the complexity of L itself. Further, there is a deterministic context-free language L for which L{DAGREACH is LogCFL- complete. We use L{REACH as a lens to study structural complexity. In this direction we show that there is a language A in TC0 for which A{DAGREACH is NP-complete. Using this we show that P vs NP question is equivalent to P vs DAGREACH-1(P)¹ question. This leads to the intriguing possibility that by proving DAGREACH-1(P) is contained in some subclass of P, we can prove an upward translation of separation of complexity classes. Note that we do not know a way to upward translate the separation of complexity classes. [ABSTRACT FROM AUTHOR] |
| Copyright of Fundamenta Informaticae is the property of Polskie Towarzystwo Matematyczne and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Databáze: | Complementary Index |
Nájsť tento článok vo Web of Science Buďte první, kdo okomentuje tento záznam!