Article Free Access Share on Some classes of multilevel relational structures Authors: Dirk Van Gucht Indiana University at Bloomington Indiana University at BloomingtonView Profile , Patrick C Fischer Vanderbilt University Vanderbilt UniversityView Profile Authors Info & Claims PODS '86: Proceedings of the fifth ACM SIGACT-SIGMOD symposium on Principles of database systemsJune 1985 Pages 60–69https://doi.org/10.1145/6012.15405Online:01 June 1985Publication History 11citation227DownloadsMetricsTotal Citations11Total Downloads227Last 12 Months0Last 6 weeks0 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

(WlVDs) mre introduced by Jaeschke ind Scheck in order to characterize when twc NEST operations on different single attributes muld conmute [JSI. Thomas extended this result to nesting cn arbitrary

The problem of determining, given a set of multivalued dependencies, whether or not they logically imply a given join dependency is shown to be computationally intractable.

Let $\mathcal {P}_{g(n)} $ denote the class of languages acceptable by polynomial-time bounded Turing machines making at most $g(n)$ nondeterministic moves on inputs of length n. For any constructible $g(n)$,$\mathcal {P} \subseteq \mathcal {P}_{g(n)} \subseteq \mathcal {N}\mathcal {P}$The classes $\mathcal {P}_{g(n)} $, for various $g(n)$ of the form $(\log n)^k ,k \geqq 1$, are relativized and the relationships among those relativized classes are studied. In particular, oracle sets are constructed which (1) make all the relativized classes equal (this follows from Baker, Gill and Solovay (1975)); (2) make all the classes associated with powers of $\log n$ different; (3) for any k, make all the classes below $(\log n)^k $ different while the kth power class is equal to relativized $\mathcal {NP}$. Results regarding closure of the $(\log n)^k $ classes under complementation are also given.

Nondeterminism is one of the most elusive concepts in computing.

A predecessor machine is a random-access machine with a predecessor operation (i.e., an instruction which subtracts 1 from the contents of a memory cell), but with no operation which can increase the contents of a cell. A regressing function is a total function which never yields an output larger than the maximum of its inputs and a constant. Unlike the situation for random-access machines with a successor operation, it does not matter whether or not predecessor machines with loop control also have conditional transfer instructions. Furthermore, the class of functions computable by predecessor loop machines consists of exactly those regressing functions which are computable by a deterministic linear-bounded automaton. Some generalized predecessor machines are also considered.

The main result of this paper is that, given a Turing machine with several readwrite heads per tape, one can effectively construct an equivalent multitape Turing machine with a single read-write head per tape, which runs at precisely the same speed.This result implies that serial storage may be used to handle files requiring several points of immediate two-way read-write access without interruptions for rewinds, etc.It also yields simplified proofs of several results in the literature of computational complexity.

The complexity of a computable function can be measured by considering the time or space required to compute its values. Particular notions of time and space arising from variants of Turing machines have been investigated by R. W. Ritchie [14], Hartmanis and Stearns [8], and Arbib and Blum [1], among others. General properties of such complexity measures have been characterized axiomatically by Rabin [12], Blum [2], Young [16], [17], and McCreight and Meyer [10]. In this paper the speed-up and super-speed-up theorems of Blum [2] are generalized to speed-up by arbitrary total effective operators. The significance of such theorems is that one cannot equate the complexity of a computable function with the running time of its fastest program, for the simple reason that there are computable functions which in a very strong sense have no fastest programs. Let φi be the ith partial recursive function of one variable in a standard Gödel numbering of partial recursive functions. A family Φ0, Φ1, … of functions of one variable is called a Blum measure on computation providing (1) domain (φi) = domain (Φi), and (2) the predicate [Φi(x) = m] is recursive in i, x and m. Typical interpretations of Φi(x) are the number of steps required by the ith Turing machine (in a standard enumeration of Turing machines) to converge on input x, the space or number of tape squares required by the ith Turing machine to converge on input x (with the convention that Φi(x) is undefined even if the machine fails to halt in a finite loop), and the length of the shortest derivation of the value of φi(x) from the ith set of recursive equations.

A Post machine is a Turing machine which cannot both write and move on the same machine step. It is shown that the halting problem for the class of 2-state Post machines is solvable. Thus, there can be no universal 2-state Post machine. This is in contrast with the result of Shannon that there exist universal 2-state Turing machines when the machines are capable of both writing and moving on the same step.

A construction is given of a one-dimensional iterative of finite-state sequential machines, which can generate in real time the binary sequence representing the set of prime numbers.

Turing's original quintuple formalism for an abstract computing machine is compared with the quadruple approach of Post and with some new alterr~atives.In each case the possibility or nmipossibility of two--symbol or two-state ~miversal machines is demon.strated.