信息与控制最新文献

Parallel algorithms are normally designed for execution on networks of N processors, with N depending on the size of the problem to be solved. In practice there will be a varying problem size but a fixed network size. In Fishburn and Finkel (IEEE Trans. Comput. 31 (1982), 288–295), the notion of network emulation was proposed, to obtain a structure preserving simulation of large networks on smaller networks. We present a detailed analysis of the possible emulations for some important classes of networks, namely: the shuffle-exchange network, the cube network, the ring network, and the 2-dimensional grid. We also study the possibility of cross-emulations, and characterize the networks that can be emulated at all on a given network using some class of emulation functions.

An oracle X is constructed such that the exponential complexity class Δ^EP,X₂ equals the probabilistic class R(R(X)). This shows that it will be difficult to prove that Δ^EP₂ is different from R(R), although it seems very unlikely that these two classes are equal. The result subsumes several known results about relativized computations:

• (i)

  the existence of relativized polynomial hierarchies extending two levels (Long, T., 1978, Dissertation, Purdue Univ., Lafayette, Ind.; Heller, H., 1984(a), SIAM J. Comput. 13, 717–725; Heller, H., 1984(b), Math. Systems Theory 17, 71–84);

• (ii)

  the existence of an oracle X such that BPP(X) ⊄ Δ^P,X₂ (Stockmeyer, L., 1983, “Proc. 15th STOC” pp. 118–126),

• (iii)

  the existence of an oracle X such that NP(X) is polynomially Turing reducible to a sparse set (Wilson, C., 1983, “Proc. 24th FOCS,”, pp. 329–334; Immerman, N., and Mahaney, S., 1983, “Conference on Computational Complexity Theory,” Santa Barbara, March 21–25).

The result shows possible inclusion relations for nonrelativized complexity classes and points out that certain results about probabilistic complexity classes and about polynomial size circuits cannot be improved unless methods are applied which do not relativize.

The frameworks of unconditional and conditional Term Rewriting and Applicative systems are explored with the objective of using them for defining functions. In particular, a new operational semantics, Tue-Reduction, is elaborated for conditional term rewriting systems. For each framework, the concept of evaluation of terms invoking defined functions is formalized. We then discuss how it may be ensured that a function definition in each of these frameworks is meaningful, by defining restrictions that may be imposed to guarantee termination, unambiguity, and completeness of definition. The three frameworks are then compared, studying when a definition may be translated from one formalism to another.

Galperin and Wigderson (Inform. and Control 56 (1983), 183–198) showed that certain trivial graph properties become NP-complete when the graph is represented in a particular exponentially succinct way. We show that under the same representation, graph properties that are ordinarily NP-complete become complete for non-deterministic exponential time.

Systolic trellis automata are models of hexagonally connected and triangularly shaped systolic arrays. This paper studies the problems of stability, decidability, and complexity for them. The original definition of systolic trellis automata requires that an input string is fed to a specific row of processors. Here it is shown that given a homogeneous trellis automaton we can construct an equivalent one (stable or superstable) which allows to feed the input string to any sufficiently long row of processors. Moreover, some closure and decidability results for trellis automata are established and the computational complexity of languages accepted by trellis automata is investigated.

This paper deals with categorical models of the λ-calculus. We generalize the inverse limit method Scott used for his construction of D_∞, and introduce order-enriched ccc's, retraction map categories and ɛ-categories. An order-enriched ccc is a cartesian closed category C equipped with a partial order relation ⩽ on the set of the arrows. A retraction map category of C is R=(R, ⩽, i, j), where ⩽ is a partial order relation on the set |C| of all the objects of C, R is the category of the poset (|C|, ⩽), and i and j are functors from R to C and from R^op to C that satisfy the conditions: (1) j a, b ∘ i a, b ⩾ id_a and (2) i a, b ∘ j a, b ⩽ id_b for every arrow a, b: a → b in R (i.e., a⩽b). The ɛ-category E=E(C, R) of C w.r.t. R is the category whose objects are ideals of (|C|, ⩽) and whose arrows are ideals of (C, ⊑), where ⩽ is the partial order relation in R and ⊑ is the partial order relation defined by f ⊑ g iff dom(f)⩽dom(g), cod(f)⩽cod(g) in R and f⩽j a, b ∘ g ∘ i(a, b in C. We show that every ɛ-category E=E(C, R) is also an order-enriched ccc. Moreover when E and R satisfy a particular condition, E(C, R) has a reflexive object. For example, if there is an ideal U of (|C|, ⩽) satisfying the following conditions, then U is isomorphic to U^U in E and a λ-algebra is constructed from E and U: (1) for every pair of a, b ∈ U, U contains b^a, and (2) for every c ∈ U, there are a, b ∈ U such that c ∈ b^a. We reconstruct P_ω and D_∞ using ɛ-categories.

Borodin, Cook, and Pippenger (Inform. and Control 58 (1983), 96–114) proved that both probabilistic acceptors and transducers working in space S(n) ⩾ log n can be simulated by deterministic machines in O(S(n)²) space. The definition of probabilistic computations uses one-way read-only random tape. Borodin et al. asked: “Is it possible to extend our simulation results to the case of a two-way read-only oracle head?” In the same vein Furst, Lipton, and Stockmeyer (Inform. and Control 64 (1985), 43–51) suggested that it could be a difference between two-way and one-way random tape: “…for space bounded probabilistic computations where the space bound is much less than the length of y, it could matter.” (y denoting the random tape inscription.) In this paper we give a full characterization of two-way random space classes that answers both questions. Karpinski and Verbeek (“There is no Polynomial Deterministic Space Simulation of Probabilistic Space with Two-way Random-Tape Generator,” Inform. and Control 67 (1985), 158–162) proved that there is no polynomial deterministic space simulation of two-way random space without giving any recursive upper bound. The results of this paper solved the open questions of Karpinski and Verbeek, 1985, Karpinski and Verbeek, 1985 and gave full characterization in sense of upper and lower deterministic space classes: they are proved precisely exponentially more powerful than the corresponding one-way classes.

This paper gives an automata-theoretical characterization of the OI-hierarchy (Damm (1982), Engelfriet and Schmidt (1977), Wand (1975)). This hierarchy is generated by so-called level-n grammars which are natural generalizations from context free and macro grammars in that their nonterminals are treated as functionals of higher type, i.e., they are allowed to carry up to n levels of parameters. The automata model used for this characterization is the n-iterated pushdown automaton. Its characteristic feature is the storage structure which consists of a nesting of pushdowns up to nesting depth n. The equivalence proof is given constructively, its method is illustrated using examples. By viewing level-n grammars as modeling recursive procedures on higher types the iterated pushdown automation thus provides an operational model for the run-time behavior of procedures defined by recursion on higher types which makes the results of this paper interesting not only from a language theoretical point of view.