scholarly journals Cost Recurrences for DML Programs

2001 ◽  
Vol 8 (25) ◽  
Author(s):  
Bernd Grobauer
Keyword(s):  
Upper Bound ◽  
Complexity Analysis ◽  
Intermediate Step ◽  
Dependent Types ◽  
Conservative Extension ◽  
Running Time ◽  
Size Information ◽  
First Order

A cost recurrence describes an upper bound for the running time of a program in terms of the size of its input. Finding cost recurrences is a frequent intermediate step in complexity analysis, and this step requires an abstraction from data to data size. In this article, we use information contained in dependent types to achieve such an abstraction: Dependent ML (DML), a conservative extension of ML, provides dependent types that can be used to associate data with size information, thus describing a possible abstraction. We systematically extract cost recurrences from first-order DML programs, guiding the abstraction from data to data size with information contained in DML type derivations.

Relativized realizability in intuitionistic arithmetic of all finite types

1978 ◽  
Vol 43 (1) ◽  
pp. 23-44 ◽  
Author(s):  
Nicolas D. Goodman
Keyword(s):  
Extension Theorem ◽  
General Notion ◽  
Conservative Extension ◽  
First Order ◽  
New Information ◽  
Reflection Theorem ◽  
Order Arithmetic ◽  
Special Case ◽  
Dependent Choice ◽  
Intuitionistic Arithmetic

In this paper we introduce a new notion of realizability for intuitionistic arithmetic in all finite types. The notion seems to us to capture some of the intuition underlying both the recursive realizability of Kjeene [5] and the semantics of Kripke [7]. After some preliminaries of a syntactic and recursion-theoretic character in §1, we motivate and define our notion of realizability in §2. In §3 we prove a soundness theorem, and in §4 we apply that theorem to obtain new information about provability in some extensions of intuitionistic arithmetic in all finite types. In §5 we consider a special case of our general notion and prove a kind of reflection theorem for it. Finally, in §6, we consider a formalized version of our realizability notion and use it to give a new proof of the conservative extension theorem discussed in Goodman and Myhill [4] and proved in our [3]. (Apparently, a form of this result is also proved in Mine [13]. We have not seen this paper, but are relying on [12].) As a corollary, we obtain the following somewhat strengthened result: Let Σ be any extension of first-order intuitionistic arithmetic (HA) formalized in the language of HA. Let Σω be the theory obtained from Σ by adding functionals of finite type with intuitionistic logic, intensional identity, and axioms of choice and dependent choice at all types. Then Σω is a conservative extension of Σ. An interesting example of this theorem is obtained by taking Σ to be classical first-order arithmetic.

Limit Cycle Bifurcations for Piecewise Smooth Hamiltonian Systems with a Generalized Eye-Figure Loop

2016 ◽  
Vol 26 (12) ◽  
pp. 1650204 ◽  
Author(s):  
Jihua Yang ◽  
Liqin Zhao
Keyword(s):  
Lower Bound ◽  
Limit Cycle ◽  
Hamiltonian Systems ◽  
Limit Cycles ◽  
Upper Bound ◽  
Melnikov Function ◽  
Piecewise Smooth ◽  
First Order ◽  
Period Annulus

This paper deals with the limit cycle bifurcations for piecewise smooth Hamiltonian systems. By using the first order Melnikov function of piecewise near-Hamiltonian systems given in [Liu & Han, 2010], we give a lower bound and an upper bound of the number of limit cycles that bifurcate from the period annulus between the center and the generalized eye-figure loop up to the first order of Melnikov function.

Designing Document SQL (DSQL)

2009 ◽  
Vol 20 (4) ◽  
pp. 26-53 ◽  
Author(s):  
Arijit Sengupta ◽  
V. Ramesh
Keyword(s):  
Ad Hoc ◽  
Query Language ◽  
Optimization Techniques ◽  
Order Logic ◽  
Conservative Extension ◽  
Tree Structures ◽  
First Order ◽  
Easy Integration ◽  
Query Semantics ◽  
Theoretical Foundations

This article presents DSQL, a conservative extension of SQL, as an ad-hoc query language for XML. The development of DSQL follows the theoretical foundations of first order logic, and uses common query semantics already accepted for SQL. DSQL represents a core subset of XQuery that lends well to optimization techniques, while at the same time allows easy integration into current databases and applications that useSQL. The intent of DSQL is not to replace XQuery, the current W3C recommended XML query language, but to serve as an ad-hoc querying frontend to XQuery. Further, the authors present proofs for important query language properties such as complexity and closure. An empirical study comparing DSQL and XQuery for the purpose of ad-hoc querying demonstrates that users perform better with DSQL for both flat and tree structures, in terms of both accuracy and efficiency.

LEAST MEAN SQUARED BACKGROUND CALIBRATION FOR OFDM MULTICHANNEL RECEIVERS

2012 ◽  
Vol 21 (01) ◽  
pp. 1250014
Author(s):  
KRISHNA PENTAKOTA ◽  
MARIO A. RAMIREZ ◽  
SEBASTIAN HOYOS
Keyword(s):  
Filter Banks ◽  
Complexity Analysis ◽  
Wide Band ◽  
Lms Algorithm ◽  
First Order ◽  
Calibration Algorithm ◽  
Estimation Scheme ◽  
Lower Complexity ◽  
Charge Sampling ◽  
Data Estimation

This paper presents a data estimation scheme for wide band multichannel charge sampling filter bank receivers together with a complete system calibration algorithm based on the least mean squared (LMS) algorithm. A unified model has been defined for the receiver containing all first order mismatches, offsets, imperfections, and the LMS algorithm is employed to track these errors. The performance of this technique under noisy channel conditions has been verified. Moreover, a detailed complexity analysis of the calibration algorithm is provided which shows that sinc filter banks have much lower complexity than traditional continuous-time filter banks.

Some properties of epistemic set theory with collection

1986 ◽  
Vol 51 (3) ◽  
pp. 748-754 ◽  
Author(s):  
Andre Scedrov
Keyword(s):  
Set Theory ◽  
Intuitionistic Logic ◽  
Existential Quantifier ◽  
Modal Interpretation ◽  
Conservative Extension ◽  
Disjunction Property ◽  
First Order ◽  
Slight Extension ◽  
Order Arithmetic ◽  
Epistemic Systems

Myhill [12] extended the ideas of Shapiro [15], and proposed a system of epistemic set theory IST (based on modal S4 logic) in which the meaning of the necessity operator is taken to be the intuitive provability, as formalized in the system itself. In this setting one works in classical logic, and yet it is possible to make distinctions usually associated with intuitionism, e.g. a constructive existential quantifier can be expressed as (∃x) □ …. This was first confirmed when Goodman [7] proved that Shapiro's epistemic first order arithmetic is conservative over intuitionistic first order arithmetic via an extension of Gödel's modal interpretation [6] of intuitionistic logic.Myhill showed that whenever a sentence □A ∨ □B is provable in IST, then A is provable in IST or B is provable in IST (the disjunction property), and that whenever a sentence ∃x.□A(x) is provable in IST, then so is A(t) for some closed term t (the existence property). He adapted the Friedman slash [4] to epistemic systems.Goodman [8] used Epistemic Replacement to formulate a ZF-like strengthening of IST, and proved that it was a conservative extension of ZF and that it had the disjunction and existence properties. It was then shown in [13] that a slight extension of Goodman's system with the Epistemic Foundation (ZFER, cf. §1) suffices to interpret intuitionistic ZF set theory with Replacement (ZFIR, [10]). This is obtained by extending Gödel's modal interpretation [6] of intuitionistic logic. ZFER still had the properties of Goodman's system mentioned above.

A second order version of S2i and U21

1991 ◽  
Vol 56 (3) ◽  
pp. 1038-1063 ◽  
Author(s):  
Gaisi Takeuti
Keyword(s):  
Second Order ◽  
The Other ◽  
Polynomial Hierarchy ◽  
Bounded Arithmetic ◽  
Conservative Extension ◽  
First Order ◽  
Second Order Systems ◽  
Separation Problems

In [1] S. Buss introduced systems of bounded arithmetic , , , (i = 1, 2, 3, …). and are first order systems and and are second order systems. and are closely related to and respectively in the polynomial hierarchy, and and are closely related to PSPACE and EXPTIME respectively. One of the most important problems in bounded arithmetic is whether the hierarchy of bounded arithmetic collapses, i.e. whether = or = for some i, or whether = , or whether is a conservative extension of S2 = ⋃i. These problems are relevant to the problems whether the polynomial hierarchy PH collapses or whether PSPACE = PH or whether PSPACE = EXPTIME. It was shown in [4] that = implies and consequently the collapse of the polynomial hierarchy. We believe that the separation problems of bounded arithmetic and the separation problems of computational complexities are essentially the same problem, and the solution of one of them will lead to the solution of the other.

Bifurcation of Limit Cycles in a Near-Hamiltonian System with a Cusp of Order Two and a Saddle

2016 ◽  
Vol 26 (11) ◽  
pp. 1650180 ◽  
Author(s):  
Ali Bakhshalizadeh ◽  
Hamid R. Z. Zangeneh ◽  
Rasool Kazemi
Keyword(s):  
Asymptotic Expansion ◽  
Hamiltonian System ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Upper Bound ◽  
Melnikov Function ◽  
Bifurcation Of Limit Cycles ◽  
Heteroclinic Loop ◽  
First Order ◽  
Period Annulus

In this paper, the asymptotic expansion of first-order Melnikov function of a heteroclinic loop connecting a cusp of order two and a hyperbolic saddle for a planar near-Hamiltonian system is given. Next, we consider the limit cycle bifurcations of a hyper-elliptic Liénard system with this kind of heteroclinic loop and study the least upper bound of limit cycles bifurcated from the period annulus inside the heteroclinic loop, from the heteroclinic loop itself and the center. We find that at most three limit cycles can be bifurcated from the period annulus, also we present different distributions of bifurcated limit cycles.

Epistemic arithmetic is a conservative extension of intuitionistic arithmetic

1984 ◽  
Vol 49 (1) ◽  
pp. 192-203 ◽  
Author(s):  
Nicolas D. Goodman
Keyword(s):  
Propositional Calculus ◽  
Cut Elimination ◽  
Conservative Extension ◽  
First Order ◽  
Classical Mathematics ◽  
Order Arithmetic ◽  
Classical Propositional Calculus ◽  
Epistemic Arithmetic ◽  
Classical Arithmetic ◽  
Intuitionistic Arithmetic

Questions about the constructive or effective character of particular arguments arise in several areas of classical mathematics, such as in the theory of recursive functions and in numerical analysis. Some philosophers have advocated Lewis's S4 as the proper logic in which to formalize such epistemic notions. (The fundamental work on this is Hintikka [4].) Recently there have been studies of mathematical theories formalized with S4 as the underlying logic so that these epistemic notions can be expressed. (See Shapiro [7], Myhill [5], and Goodman [2]. The motivation for this work is discussed in Goodman [3].) The present paper is a contribution to the study of the simplest of these theories, namely first-order arithmetic as formalized in S4. Following Shapiro, we call this theory epistemic arithmetic (EA). More specifically, we show that EA is a conservative extension of Hey ting's arithmetic HA (ordinary first-order intuitionistic arithmetic). The question of whether EA is conservative over HA was raised but left open in Shapiro [7].The idea of our proof is as follows. We interpret EA in an infinitary propositional S4, pretty much as Tait, for example, interprets classical arithmetic in his infinitary classical propositional calculus in [8]. We then prove a cut-elimination theorem for this infinitary propositional S4. A suitable version of the cut-elimination theorem can be formalized in HA. For cut-free infinitary proofs, there is a reflection principle provable in HA. That is, we can prove in HA that if there is a cut-free proof of the interpretation of a sentence ϕ then ϕ is true. Combining these results shows that if the interpretation of ϕ is provable in EA, then ϕ is provable in HA.

scholarly journals GEOMETRISATION OF FIRST-ORDER LOGIC

2015 ◽  
Vol 21 (2) ◽  
pp. 123-163 ◽  
Author(s):  
ROY DYCKHOFF ◽  
SARA NEGRI
Keyword(s):  
Proof Theory ◽  
Normal Forms ◽  
Order Theory ◽  
Order Logic ◽  
First Order Logic ◽  
Conservative Extension ◽  
First Order ◽  
First Order Theory ◽  
Intermediate Logics ◽  
Normal Form Theorem

AbstractThat every first-order theory has a coherent conservative extension is regarded by some as obvious, even trivial, and by others as not at all obvious, but instead remarkable and valuable; the result is in any case neither sufficiently well-known nor easily found in the literature. Various approaches to the result are presented and discussed in detail, including one inspired by a problem in the proof theory of intermediate logics that led us to the proof of the present paper. It can be seen as a modification of Skolem’s argument from 1920 for his “Normal Form” theorem. “Geometric” being the infinitary version of “coherent”, it is further shown that every infinitary first-order theory, suitably restricted, has a geometric conservative extension, hence the title. The results are applied to simplify methods used in reasoning in and about modal and intermediate logics. We include also a new algorithm to generate special coherent implications from an axiom, designed to preserve the structure of formulae with relatively little use of normal forms.

scholarly journals Properties of antithrombin-thrombin complex formed in the presence and in the absence of heparin

1983 ◽  
Vol 213 (2) ◽  
pp. 345-353 ◽  
Author(s):  
A Danielsson ◽  
I Björk
Keyword(s):  
Rate Constants ◽  
Gel Electrophoresis ◽  
Polyacrylamide Gel Electrophoresis ◽  
Dissociation Rate ◽  
Exchange Chromatography ◽  
Stable Complex ◽  
Intermediate Step ◽  
First Order ◽  
Activity Measurements ◽  
Dissociation Rate Constants

Purification of antithrombin-thrombin complex by ion-exchange chromatography on DEAE-agarose resulted in predominantly monomeric complex, whereas purification on matrix-linked heparin produced large amounts of aggregated complex. Monomeric antithrombin-thrombin complexes formed in the presence and in the absence of heparin had similar conformations and heparin affinities. Moreover, the first-order dissociation rate constants, measured by thrombin release, of these complexes were similar, 2.3 × 10(-6)-3.4 × 10(-6)S-1, regardless of whether newly formed or purified complex was analysed. Similar dissociation rate constants were also obtained for purified complex formed with or without heparin, from analyses by dodecyl sulphate/polyacrylamide-gel electrophoresis of the release of modified antithrombin, cleaved at the reactive-site bond. No dissociation of intact antithrombin from the complex was detected by activity measurements or by gel electrophoresis. Aggregation of the complex was found to be accompanied by a decrease in apparent dissociation rate. The similar properties of antithrombin-thrombin complexes formed with or without heparin support the concept of a catalytic role for the polysaccharide in the antithrombin-thrombin reaction. Furthermore, the results indicate that the reaction between enzyme and inhibitor involves the rapid formation of an irreversible, kinetically stable, complex that dissociates into active thrombin and modified, inactive, antithrombin by a first-order process with a half-life of about 3 days. The inhibition thus resembles a normal proteolytic reaction, one intermediate step of which is very slow.

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