D.S. Johnson. A catalog of complexity classes. Handbook of Theoretical Computer Science, A:67--161, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....2 L iff f(x) 0. Theorem 8 immediately implies that these definitions coincide with ours, which is exactly the statement of Theorem 3. Bounded error and one sided error circuit based probabilistic complexity classes were defined in the literature for the classes in the AC and NC hierarchy [Weg87,Joh90,Coo85] These are semantical definitions in our terminology, but unlike in our case, no special restriction is put on the way counting variables are introduced. To be more precise, let a probabilistic circuit family (Cn ) be defined as a uniform family of circuits where the circuits have standard ....

D.S. Johnson. A catalog of complexity classes. Handbook of Theoretical Computer Science, A:67--161, 1990.

....if for each pomset isomorphism Gamma and each pomset P , Q( Gamma (P ) Gamma (Q(P ) We consider the data complexity of queries, i.e. the complexity of the evaluation of a query in terms of the size of the input databases. The size is defined with respect to a standard encoding [AHV94, Joh90] The standard encoding of a pomset p is based on some labeled partial order (V; Sigma; and is similar to that of the binary relations representing and . Note that in this encoding, each object in Sigma, is repeated as many times as the vertices it labels in V . The size is therefore ....

D.S. Johnson. Handbook of Theoretical Computer Science, volume A, chapter A catalog of complexity classes, pages 67--162. North Holland, J. Van Leeuwen Ed., 1990.

....of circuit size as a nonuniform complexity measure. They also introduced the class P=poly for characterizing the class of languages having polynomialsize circuits. Though P=poly is de ned in a di erent way, in this paper, we use the following rather intuitive de nition for P=poly. See, e.g. [BDG88, Joh90]) Definition 3.1. A set A has polynomial size circuits if there exist a polynomial p and a family fC n g n0 of circuits such that for each n 0, i) C n takes a string x of length n as input and determines whether x is in A, and (ii) the size of C n is bounded by p(n) Let P=poly be the class of ....

Johnson D. A catalog of complexity classes. Handbook of Theoretical Computer Science (Van Leeuwen, Ed.), Elsevier 1990:67-161.

....in this area. The computational complexity of Th(R; is investigated in [19, 45, 92, 119] The complexity of Th(R; a subset of the previous theory, is in DSPACE(2 cn ) where n is the size of the formula [55] and also in alternating Turing machine class TA(2 cn ; n) 29] See [77] for definitions of various complexity classes. Another interesting subset of the above theory allows only difference constraints, i.e. only constraints of the form x i Gamma x j c for x i ; x j variables and c constant. The complexity of this language is considered in [90, 91] and is shown ....

D.S. Johnson. A Catalogue of Complexity Classes. Handbook of Theoretical Computer Science, Vol. A, chapter 2, (J. van Leeuwen editor), NorthHolland, 1990.

....of circuit size as a nonuniform complexity measure. They also introduced the class P=poly for characterizing the class of languages having polynomialsize circuits. Though P=poly is defined in a different way, in this paper, we use the following rather intuitive definition for P=poly. See, e.g. [BDG88, Joh90]) Definition 3.1. A set A has polynomial size circuits if there exist a polynomial p and a family fC n g n0 of circuits such that for each n 0, i) C n takes a string x of length n as input and determines whether x is in A, and (ii) the size of C n is bounded by p(n) Let P=poly be the class of ....

Johnson D. A catalog of complexity classes. Handbook of Theoretical Computer Science (Van Leeuwen, Ed.), Elsevier 1990:67--161.

....comparison. For instance, if we are given a composite number and asked to find a witness to its compositeness (a divisor) we may verify this relation in one step. Finding such a divisor is at least of polynomial complexity. There is no known polynomial algorithm to test if a number is composite [Joh90]. We now provide an EPC that forces self stabilization onto programs that take a constant number of steps. In order to do so we must make the following enhancement to our model which does not exist in EQL. We assume that the 28 Chapter 2 assignment expression in a rule can contain nested ....

D. Johnson. A Catalog of Complexity Classes. Handbook of Theoretical Computer Science, Vol. A, North-Holland, Amsterdam, 1990

....Thus, we analyze in detail the consistency problem for monadic and or recursion free method schemas, which happen to be decidable. We also quantify the effect of covariance, which is a widely used constraint on the signature of methods. For the various concepts used from complexity theory, see [15, 19, 20, 29] and from database theory, see [21, 30] We briefly summarize our other results. Let n be the size of method definitions in the input method schema and c the size of the class hierarchy. In the case of monadic schemas, the set of possible computations can be described using a context free ....

....fact that NLOGSPACE is closed under complement [19, 29] and conclude that consistency is in NLOGSPACE. Finally, we show that consistency of simple, monadic schemas is hard using a reduction of the reachability problem for graphs of out degree 2 which is known to be logspace complete in NLOGSPACE [20]. Let G = V; E) be a graph where each vertex has out degree exactly 2; and for each w in V , let f(w) and g(w) be the two successors of w. Let v; v 0 be in V . The problem is to decide whether there is a path from v to v 0 . We exhibit a schema S = C; Sigma 0 ; Sigma 1 ) such that ....

[Article contains additional citation context not shown here]

D.S. Johnson. A Catalog of Complexity Classes. Handbook of Theoretical Computer Science, Vol. A, Chapter 2, (J. van Leeuwen, A.R. Meyer, N. Nivat, M.S. Paterson, D. Perrin editors), North-Holland, 1990.

....parts that can grow asymptotically versus the parts that are constant size. By fixing the program size and letting the database grow, one can prove that the evaluation can be performed in PTIME or in NC or in LOGSPACE, depending on the constraints considered (for the various complexity classes see [38]) 1.4 Languages, efficiency, efficiency, In the remainder of this paper we explore CQLs with an emphasis on quantifying language efficiency. In Section 2, we present an algebra for dense order constraints (due to Goldin) which is simpler to evaluate than the calculus described in [41] In ....

....NC) if there is a TM (resp. TM, PRAM) which given input generalized relations d produces some generalized relation representing the output of Q(d) and uses polynomial time (resp. logarithmic space on the work tape, polynomial number of processors running in polylogarithmic parallel time) See [38] for definitions of TMs and PRAMs. We assume a standard binary encoding of generalized relations. The CQL framework is interesting because many combinations of database query languages and decidable theories have PTIME data complexity. From Codd s original work [20] it follows that: relational ....

D.S. Johnson. A Catalogue of Complexity Classes. Handbook of Theoretical Computer Science, Vol. A, chapter 2, (J. van Leeuwen editor), North-Holland, 1990.

....a DLOGSPACE complexity query is not expressible in NRC aggr . If it could be shown that the complexity of NRC aggr queries is in a class that is strictly lower than DLOGSPACE and does not con4 tain the parity test, then we would have solved conjecture 1. It is known that AC 0 ae DLOGSPACE [FSS84, Joh90]. Queries written in NRC have AC 0 data complexity [ST94] This inclusion implies that the parity test (is the cardinality of a set even ) and the transitive closure cannot be expressed in NRC because they can not be done within AC 0 [FSS84, Joh90] If NRC aggr had AC 0 data complexity, ....

....1. It is known that AC 0 ae DLOGSPACE [FSS84, Joh90] Queries written in NRC have AC 0 data complexity [ST94] This inclusion implies that the parity test (is the cardinality of a set even ) and the transitive closure cannot be expressed in NRC because they can not be done within AC 0 [FSS84, Joh90]. If NRC aggr had AC 0 data complexity, the same argument would solve at least conjectures 1 and 2. However, it is not hard to see that there are nonAC 0 queries that one can write in NRC aggr since multiplication is not in AC 0 [FSS84] As a more interesting example of a non AC 0 ....

D. Johnson. A Catalog of Complexity Classes, Handbook of Theoretical Computer Science, volume A, chapter 2, pages 67--161. North Holland, 1990.

....circuit size as a nonuniform complexity measure. They also introduced the class P=poly for characterizing the class of languages having polynomial size circuits. Though P=poly is defined in a different way, in this paper, we use the following rather intuitive definition for P=poly. See, e.g. [BDG88, Joh90]) Definition 3.1. A set A has polynomial size circuits if there exist a polynomial p and a family fC n g n0 of circuits such that for each n 0, i) C n takes a string x of length n as input and determines whether x is in A, and (ii) the size of C n is bounded by p(n) Let P=poly be the class ....

Johnson D. A catalog of complexity classes. Handbook of Theoretical Computer Science (Van Leeuwen, Ed.), Elsevier 1990:67--161.

....Thus, we analyze in detail the consistency problem for monadic and or recursion free method schemas, which happen to be decidable. We also quantify the effect of covariance, which is a widely used constraint on the signature of methods. For the various concepts used from complexity theory, see [15, 19, 20, 30] and from database theory, see [21, 31] We briefly summarize our other results. Let n be the size of method definitions in the input method schema and c the size of the class hierarchy. In the case of monadic schemas, the set of possible computations can be described using a context free ....

....fact that NLOGSPACE is closed under complement [19, 30] and conclude that consistency is in NLOGSPACE. Finally, we show that consistency of simple, monadic schemas is hard using a reduction of the reachability problem for graphs of out degree 2 which is known to be logspace complete in NLOGSPACE [20]. Let G = V; E) be a graph where each vertex has out degree exactly 2; and for each w in V , let f(w) and g(w) be the two successors of w. Let v; v 0 be in V . The problem is to decide whether there is a path from v to v 0 . We exhibit a schema S = C; Sigma 0 ; Sigma 1 ) such that ....

[Article contains additional citation context not shown here]

D.S. Johnson. A Catalog of Complexity Classes. Handbook of Theoretical Computer Science, Vol. A, Chapter 2, (J. van Leeuwen, A.R. Meyer, N. Nivat, M.S. Paterson, D. Perrin editors), North-Holland, 1990.

No context found.

D. S. Johnson. A Catalog of Complexity Classes, Handbook of Theoretical Computer Science, Vol. 1, J. Leewen ed. North-Holland,1990, pp.67--161.

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, "A catalog of complexity classes," in J. van Leeuwen, Ed., Handbook of Theoretical Computer Science, vol. A: Algorithms and Complexity, NorthHolland, (1990), pp. 67--161.

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