C. Alvarez and R. Greenlaw. A compendium of problems complete for symmetric logarithmic space. ECCC report TR96-039, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....color classes of size 2 and 3. We prove that 2 GA and 3 GA belong also to SL and moreover 2 GA is equivalent to the problem UCC of deciding whether a given graph has more than one connected component. UCC belongs to SL but it seems to be easier than UGAP and it is not known to be complete for SL [1]. For simplicity we have proven our hardness and equivalence results for logarithmic space many one reducibility, but in fact they hold for stronger reducibilities, like for example DLOGTIME uniform NC many one reducibility. All the graphs considered in this paper are undirected graphs. 2 ....

 Alvarez, C., Greenlaw, R.: A compendium of problems complete for symmetric logarithmic space. Journal of Computational Complexity 9 (2000) 73-95

....structure to be complete for NC . We also prove that 2 GA and 3 GA belong to SL and moreover 2 GA is equivalent to the problem UCC of deciding whether a given graph has more than one connected component. UCC belongs to SL but it seems easier than UGAP and it is not known to be complete for SL [19]. 2 Preliminaries We assume familiarity with basic notions of complexity theory such as can be found in the standard books in the area. In particular, we simply recall that NC L SL NL NC ; where AC is the class of languages recognized by DLOGTIME uniform families of ....

C.  Alvarez, R. Greenlaw, A compendium of problems complete for symmetric logarithmic space, Journal of Computational Complexity 9 (2000) 73-95.

....word problem for the class of all 2 homogeneous semi Thue systems is complete for symmetric log space. This result is in particular interesting from the viewpoint of computational complexity, since there are quite few natural and nonobvious SL complete problems in formal language theory, see [2]. 2 Preliminaries We assume some familiarity with computational complexity, see e.g. 21] in particular with circuit complexity, see e.g. 27] L denotes deterministic logarithmic space. SL (symmetric log space) is the class of all problems that can be solved in log space on a symmetric ....

....machine, see [14] for more details. Important results for SL are the closure of SL under log space bounded Turing reductions, i.e. SL = L SL [19] and the fact that problems in SL can be solved in deterministic space O(log(n) 4 3 ) 3] A collection of SL complete problems can be found in [2]. For the de nition of DLOGTIME uniformity and DLOGTIME reductions see e.g. 10, 5] DLOGTIME uniform NC 1 , brie y uNC 1 , is the class of all languages that can be recognized by a DLOGTIME uniform family of polynomial size, logarithmic depth, fan in two Boolean circuits. It is well known ....

C. Alvarez and R. Greenlaw. A compendium of problems complete for symmetric logarithmic space. Electronic Colloquium on Computational Complexity, Report No. TR96-039, 1996.

....the situation has been far from clear. The best upper bound on the complexity of planarity that has been published so far is the bound of AC 1 that follows from the logarithmic time CRCW PRAM algorithm of Ramachandran and Reif [22] In a recent survey of problems in the complexity class SL [2], the planarity problem for graphs of bounded degree is listed as belonging to SL, but this is based on the claim in [23] that checking planarity for bounded degree graphs is in the Symmetric Complementation Hierarchy , and on the fact that SL is closed under complement [20] and thus this ....

....w connected in G but not in G u ) 4. Is there is a path (not necessarily simple) of odd length between vertices s and t (Make two copies of each vertex. Replace edge (u, v) by edges (u0, v1) and (u1, v0) Check if s0, t1 are connected in this new graph. 5. Is G bipartite (i.e. 2 colorable) [23, 20, 2]. 6. If G is connected, 2 colorable, and vertex 1 is colored 1, is vertex i colored 2 (Test if there is a path of odd length from 1 to i. 7. Is edge e in the lexicographically first spanning tree T of G (under the standard ordering of edges) 20] Given a graph G and a spanning tree T , the ....

[Article contains additional citation context not shown here]

C. Alvarez and R. Greenlaw. A compendium of problems complete for symmetric logarithmic space. Technical Report ECCC-TR96-039, Electronic Colloquium on Computational Complexity, 1996.

.... for one of the following classes: NP, P, NL, SL, PhiL (as it turns out this is not Schaefer s original statement, but a modern rephrasing that is based on a number of recent results, such as the closure of NL and SL under complement [Imm88, Sze88, NTS95] the complexity of graph bipartiteness [AG96], and the completeness for PhiL of the consistency problem for systems of linear binary equations [BDHM92] Definition 2.2 A k ary relation R is 2 symmetric if there is a partition fA 1 ; A p ; B 1 ; B l g of its variables (such that, for every 1 i p, jA i j = 1, and for ....

C. ' Alvarez and R. Greenlaw. A compendium of problems complete for symmetric logarithmic space. Technical Report TR96-039, Electronic Colloquium on Computational Complexity, http://www.eccc.uni-trier.de/eccc/, 1996.

No context found.

C. Alvarez and R. Greenlaw. A compendium of problems complete for symmetric logarithmic space. ECCC report TR96-039, 1996.

No context found.

C Alvarez and R Greenlaw. A compendium of problems complete for symmetric logarithmic space. Computational Complexity, 9:73--95, 2000.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC