1922 June 1995
Filter Results

Proceedings of Structure in Complexity Theory. Tenth Annual IEEE Conference
Publication Year: 1995 PDF (186 KB) 
Author index
Publication Year: 1995 PDF (37 KB) 
Towards averagecase complexity analysis of NP optimization problems
Publication Year: 1995, Page(s):148  159
Cited by: Papers (2)  Patents (1)For the worstcase complexity measure, if P=NP, then P=OptP, i.e., all NP optimization problems are polynomialtime solvable. On the other hand, it is not clear whether a similar relation holds when considering averagecase complexity. We investigate the relationship between the complexity of NP decision problems and that of NP optimization problems under polynomialtime computable distributions, ... View full abstract»

DSPACE(n)=?NSPACE(n): a degree theoretic characterization
Publication Year: 1995, Page(s):315  323
Cited by: Papers (1)It is shown that the following are equivalent: 1. DSPACE(n)=NSPACE(n). 2. There is a ⩽_{m}^{1NL}degree that coincides with a ⩽_{m}^{1L} degree. 3. For every class C closed under logspace reductions the ⩽_{m}^{1NL}complete degree of C coincides with the ⩽_{m}^{1L}complete degree of C View full abstract»

Semiunbounded fanin circuits: Boolean vs. arithmetic
Publication Year: 1995, Page(s):82  87
Cited by: Papers (4)We prove that polynomial size semiunbounded fanin Boolean circuits of depth d can be simulated by polynomial size semiunbounded fanin arithmetic circuits of depth O(d+log n), where the arithmetic operations +, , × are performed in an arbitrary finite field. It is impossible to achieve this via gatebygate simulation. Instead, the proof is based on a randomized reduction to “uniqu... View full abstract»

The power of local selfreductions
Publication Year: 1995, Page(s):277  285
Cited by: Papers (2)Identify a string x over {0, 1} with the positive integer whose binary representation is 1x. We say that a selfreduction is klocal if on input x all queries belong to {x1, …, xk}. We show that all klocally selfreducible sets belong to PSPACE. However, the power of klocal selfreductions changes drastically between k=2 and k=3. Although all 2locally selfreducible sets belong to MOD<... View full abstract»

A personal view of averagecase complexity
Publication Year: 1995, Page(s):134  147
Cited by: Papers (35)The structural theory of averagecase complexity, introduced by Levin (1986), gives a formal setting for discussing the types of inputs for which a problem is difficult. This is vital to understanding both when a seemingly difficult (e.g. NPcomplete) problem is actually easy on almost all instances, and to determining which problems might be suitable for applications requiring hard problems, such... View full abstract»

On the power of numbertheoretic operations with respect to counting
Publication Year: 1995, Page(s):299  314
Cited by: Papers (3)We investigate function classes ⟨P⟩f which are defined as the closure of P under the operation f and a set of known closure properties of P, e.g. summation over an exponential range. First, we examine operations f under which P is closed (i.e., ⟨P⟩f=P) in every relativization. We obtain the following complete characterization of these operations: P is clos... View full abstract»

Decision trees with AND, OR queries
Publication Year: 1995, Page(s):74  81
Cited by: Papers (2)  Patents (1)We investigate decision trees in which one is allowed to query threshold functions of subsets of variables. We are mainly interested in the case where only queries of AND and OR are allowed. This model is a generalization of the classical decision tree model. Its complexity (depth) is related to the parallel time that is required to compute Boolean functions in certain CRCW PRAM machines with only... View full abstract»

On superlinear lower bounds in complexity theory
Publication Year: 1995, Page(s):50  64
Cited by: Papers (1)The paper first surveys the neartotal lack of superlinear lower bounds in complexity theory, for “natural” computational problems with respect to many models of computation. We note that the dividing line between models where such bounds are known and those where none are known comes when the model allows nonlocal communication with memory at unit cost. We study a model that imposes ... View full abstract»

A note on genericity and biimmunity
Publication Year: 1995, Page(s):193  196
Cited by: Papers (3)Generic sets have all properties (from among a suitably chosen class) that can be enforced by finite extension arguments. In particular, pgeneric sets known to be Pbiimmune. We try to clarify the precise relationship between genericity and biimmunity by proposing an extended notion of biimmunity that exactly characterizes the pgeneric sets View full abstract»

A gametheoretic classification of interactive complexity classes
Publication Year: 1995, Page(s):227  237
Cited by: Papers (5)Gametheoretic characterisations of complexity classes have often proved useful in understanding the power and limitations of these classes. One wellknown example tells us that PSPACE can be characterized by twoperson, perfectinformation games in which the length of a played game is polynomial in the length of the description of the initial position [by Chandra et al., see Journal of the ACM, v... View full abstract»

Reductions of selfreducible sets to depth1 weighted threshold circuit classes, and sparse sets
Publication Year: 1995, Page(s):264  276
Cited by: Papers (1)Let LT1 denote the class of languages accepted by nonuniform families of polynomial size depth1 circuits with a linear weighted threshold gate at the root. We show that disjunctive selfreducible bdcylinders that manyone reduce to LT1 are in P. It follows that for C∈{NP, ModkP, PP, C=P}, if 𝒞 has a manyone hard problem in LT1 the... View full abstract»

Intractability of readonce resolution
Publication Year: 1995, Page(s):29  36
Cited by: Papers (4)Readonce resolution (ROR) is a resolution proof system in which the rule (A+x)(B+x¯)→(A+B) is applied in such a way that two clauses (A+x) and (B+x¯) are replaced by (A+B), i.e., (A+x) and (B+x¯) disappear, and any clause can never be copied. Therefore ROR runs in (nondeterministic) polynomial time and is no longer complete. It is shown that, in spite of its simplicity and wea... View full abstract»

Frequency computation and bounded queries
Publication Year: 1995, Page(s):125  132There have been several papers over the last ten years that consider the number of queries needed to compute a function as a measure of its complexity. The following function has been studied extensively in that light: FaA(x1, …, xa)=A(x1)···A(xa). We are interested in the complexity (in terms of the numb... View full abstract»

Resourcebounded genericity
Publication Year: 1995, Page(s):162  181
Cited by: Papers (2)Resourcebounded genericity concepts have been introduced by AmbosSpies, Fleischhack and Huwig (1984, 1988), Lutz (1990), and Fenner (1991). Though it was known that these concepts are incompatible, the relations among these notions were not fully understood. We survey these notions and clarify the relations among them by specifying the types of diagonalizations captured by the individual concept... View full abstract»

A small span theorem for P/PolyTuring reductions
Publication Year: 1995, Page(s):324  330
Cited by: Papers (2)This paper investigates the structure of ESPACE under nonuniform Turing reductions that are computed by polynomialsize circuits (P/PolyTuring reductions). A small span theorem is proven for such reductions. This result says that every language A in ESPACE satisfies at least one of the following two conditions. (i) The lower P/PolyTuring span of A (consisting of all languages that are P/PolyTur... View full abstract»

The isomorphism conjecture holds and oneway functions exist relative to an oracle
Publication Year: 1995, Page(s):90  101
Cited by: Papers (2)We demonstrate an oracle relative to which there are oneway functions but every paddable 1lidegree collapses to an isomorphism type, thus yielding a relativized failure of the JosephYoung (1985) conjecture (JYC). We then use this result to construct an oracle relative to which the isomorphism conjecture (IC) is true but oneway functions exist, which answers an open question of Fenner, Fortnow... View full abstract»

On finding the number of graph automorphisms
Publication Year: 1995, Page(s):288  298
Cited by: Papers (2)This paper investigates the enumerability of the function GA, the number of automorphisms of an undirected graph, in relation to the computational complexity of GI, the Graph Isomorphism problem. A function f (on graphs) is b(n)enumerable if there exists a function g∈PF such that for all nnode graphs G, g(G) lists b(n) numbers, one of which is f(G). The results in this paper show the follow... View full abstract»

Fault tolerant circuits and probabilistically checkable proofs
Publication Year: 1995, Page(s):65  73
Cited by: Papers (4)  Patents (1)We introduce a new model of fault tolerance for Boolean circuits. We consider synchronized circuits and we allow an adversary to choose a small constant fraction of the gates at each level of the circuit to be faulty. We require that even in the presence of such faults the circuit compute a “loose version” of the given function. We show that every symmetric function has a small (size O... View full abstract»

An excursion to the Kolmogorov random strings
Publication Year: 1995, Page(s):197  203
Cited by: Papers (3)We study the set of resource bounded Kolmogorov random strings: R t={xKt(x)⩾x} for t a time constructible function such that t(n)⩾2(n2) and t(n)∈2(nO(1)). We show that the class of sets that Turing reduce to Rt has measure 0 in EXP with respect to the resourcebounded measure introduced by Lutz (1992). From this we conclude that Rt View full abstract»

Optimizing TRIEs for ordered pattern matching is Π_{2} ^{P}complete
Publication Year: 1995, Page(s):238  244We consider the complexity of constructing a data structure, called TRIEs, with the minimum operational cost for the ordered pattern matching problem, a problem abstracting the essence of executing Prolog problems; a TRIE with minimal cost corresponds to a program with the minimum worst case operational cost. Based on the recent nonapproximability results developed by Arora et al. (1992) and Cond... View full abstract»

Semantics versus syntax versus computations. Machine models for type2 polynomialtime bounded functionals
Publication Year: 1995, Page(s):37  48The paper investigates analogs of the KreiselLacombeShoenfield (1957) Theorem in the context of the type2 basic feasible functionals, aka the MehlhornCook class of type2 polynomialtime functionals. We develop a direct, polynomialtime analog of effective operation, where the time bound on computations is modeled after Kapron and Cook's (1990) scheme for their basic polynomialtime functional... View full abstract»

Resourcebounded Baire category: a stronger approach
Publication Year: 1995, Page(s):182  192
Cited by: Papers (4)The paper introduces a new definition of resourcebounded Baire category in the style of Lutz (1987, 1990, 1992) . This definition gives an almostall/almostnone theory of various complexity classes. The meagerness/comeagerness of many more classes can be resolved in the new definition than in previous definitions. For example, almost no sets in EXP are EXPcomplete, and NP is PFmeager unless NP... View full abstract»

Inverting the Turing jump in complexity theory
Publication Year: 1995, Page(s):102  110
Cited by: Papers (1)The paper investigates the invertibility of certain analogs of the Turing jump operator in the polynomialtime Turing degrees. If 𝒞 is some complexity class, the 𝒞jump of a set A is the canonical 𝒞complete set relative to A. It is shown that the PSPACEjump and EXPjump operators are not invertible, i.e., there is a PSPACEhard (resp. EXPhard) set that is not ptime Turing equiva... View full abstract»