scholarly journals Is it possible to unify sequential programs?

10.29007/77z3 ◽  
2018 ◽  
Author(s):  
Tatyana Novikova ◽  
Vladimir Zakharov
Keyword(s):  
Polynomial Time ◽  
Functional Equivalence ◽  
Order Model ◽  
Sequential Programs ◽  
Unification Algorithm ◽  
First Order ◽  
Unification Problem ◽  
Set Up

We introduce a first-order model of imperative sequential programs and set up formally the unification problem in this model: given a pair of programs π<sub>1</sub> and π<sub>2</sub> find a pair of substitutions (θ<sub>1</sub>,θ<sub>2</sub>) such that the instances π<sub>1</sub>θ<sub>1</sub> and π<sub>2</sub>θ<sub>2</sub> of these programs are equivalent, i.e. compute the same function. Since functional equivalence of programs is undecidable, we choose its decidable approximation --- a strong equivalence, --- which is well-known in theory of program schemata. Our main result is a polynomial time unification algorithm for sequential programs w.r.t. strong equivalence of programs.

A first-order model of thermal lensing of laser propagation in the eye and implications for laser safety

2005 ◽  
Author(s):  
Robert J. Thomas ◽  
Rebecca L. Vincelette ◽  
Gavin D. Buffington ◽  
Amber D. Strunk ◽  
Michael A. Edwards ◽  
...  
Keyword(s):  
Thermal Lensing ◽  
Order Model ◽  
Laser Safety ◽  
First Order ◽  
Laser Propagation

Application of two approaches to model chlorine residuals in Severn Trent Water Ltd (STW) distribution systems

1997 ◽  
Vol 36 (5) ◽  
pp. 317-324 ◽  
Author(s):  
M.J. Rodriguez ◽  
J.R. West ◽  
J. Powell ◽  
J.B. Sérodes
Keyword(s):  
Distribution System ◽  
Distribution Systems ◽  
Treatment Plant ◽  
Residual Chlorine ◽  
Ann Model ◽  
Order Model ◽  
First Order ◽  
Chlorine Decay ◽  
Artificial Neural Network Ann ◽  
Key Parameter

Increasingly, those who work in the field of drinking water have demonstrated an interest in developing models for evolution of water quality from the treatment plant to the consumer's tap. To date, most of the modelling efforts have been focused on residual chlorine as a key parameter of quality within distribution systems. This paper presents the application of a conventional approach, the first order model, and the application of an emergent modelling approach, an artificial neural network (ANN) model, to simulate residual chlorine in a Severn Trent Water Ltd (U.K.) distribution system. The application of the first order model depends on the adequate estimation of the chlorine decay coefficient and the travel time within the system. The success of an ANN model depends on the use of representative data about factors which affect chlorine evolution in the system. Results demonstrate that ANN has a promising capacity for learning the dynamics of chlorine decay. The development of an ANN appears to be justifiable for disinfection control purposes, in cases when parameter estimation within the first order model is imprecise or difficult to obtain.

scholarly journals Intermittent heat instabilities in an air plume

2016 ◽  
Vol 23 (4) ◽  
pp. 319-330
Author(s):  
Jean-Louis Le Mouël ◽  
Vladimir G. Kossobokov ◽  
Frederic Perrier ◽  
Pierre Morat
Keyword(s):  
Temperature Sensors ◽  
Time Varying ◽  
First Order ◽  
Spatial Function ◽  
Universal Feature ◽  
Classical Models ◽  
Set Up ◽  
Plume Flow ◽  
Temperature Time ◽  
Classical Shape

Abstract. We report the results of heating experiments carried out in an abandoned limestone quarry close to Paris, in an isolated room of a volume of about 400 m3. A heat source made of a metallic resistor of power 100 W was installed on the floor of the room, at distance from the walls. High-quality temperature sensors, with a response time of 20 s, were fixed on a 2 m long bar. In a series of 24 h heating experiments the bar had been set up horizontally at different heights or vertically along the axis of the plume to record changes in temperature distribution with a sampling time varying from 20 to 120 s. When taken in averages over 24 h, the temperatures present the classical shape of steady-state plumes, as described by classical models. On the contrary, the temperature time series show a rich dynamic plume flow with intermittent trains of oscillations, spatially coherent, of large amplitude and a period around 400 s, separated by intervals of relative quiescence whose duration can reach several hours. To our knowledge, no specific theory is available to explain this behavior, which appears to be a chaotic interaction between a turbulent plume and a stratified environment. The observed behavior, with first-order factorization of a smooth spatial function with a global temporal intermittent function, could be a universal feature of some turbulent plumes in geophysical environments.

Reduced Order Model of MEMS Sensors Near Natural Frequency

2011 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Jose C. Solis Silva
Keyword(s):  
Natural Frequency ◽  
Nonlinear Response ◽  
Casimir Effect ◽  
Electrostatic Force ◽  
Reduced Order Model ◽  
Mass Detection ◽  
Order Model ◽  
Reduced Order ◽  
First Order ◽  
Electrostatically Actuated

The nonlinear response of an electrostatically actuated cantilever beam microresonator sensor for mass detection is investigated. The excitation is near the natural frequency. A first order fringe correction of the electrostatic force, viscous damping, and Casimir effect are included in the model. The dynamics of the resonator is investigated using the Reduced Order Model (ROM) method, based on Galerkin procedure. Steady-state motions are found. Numerical results for uniform microresonators with mass deposition and without are reported.

First-Order Frequency Effects in Supersonic Panel Flutter of Finite Cylindrical Shells

1973 ◽  
Vol 40 (2) ◽  
pp. 464-470
Author(s):  
M. Holt ◽  
T. M. Lee
Keyword(s):  
Mach Number ◽  
Elastic Shell ◽  
Order Effect ◽  
Aerodynamic Load ◽  
Panel Flutter ◽  
Thin Cylindrical Shell ◽  
First Order ◽  
Flutter Boundary ◽  
Shell Equation ◽  
Set Up

An improved calculation of the supersonic panel flutter characteristics of a thin cylindrical shell of finite length is presented. The aerodynamic load is determined with account taken of first-order terms in vibration frequency, and when this is introduced into the elastic shell equation an integro differential equation results. An equivalent eigenvalue problem is set up by applying Galerkin’s method to this equation. The flutter boundary, for given Mach number and circumferential mode n, corresponds to the shell thickness ratio at which the real part of any one of the eigenvalues first becomes non-negative. It is found that the most severe flutter condition, for given Mach number, occurs for a circumferential mode n = 7. The present calculations exclude second-order frequency terms in the elastic part of the flutter equation, even though they may have a first-order effect. A subsequent calculation referred to here shows that these terms indeed have no significant influence on the first-order analysis.

Strong extension axioms and Shelah's zero-one law for choiceless polynomial time

2003 ◽  
Vol 68 (1) ◽  
pp. 65-131 ◽  
Author(s):  
Andreas Blass ◽  
Yuri Gurevich
Keyword(s):  
Fixed Point ◽  
Polynomial Time ◽  
Order Logic ◽  
Complexity Class ◽  
First Order Logic ◽  
Infinitary Logic ◽  
Extensive Discussion ◽  
First Order ◽  
Detailed Proof ◽  
Strong Extension

AbstractThis paper developed from Shelah's proof of a zero-one law for the complexity class “choiceless polynomial time,” defined by Shelah and the authors. We present a detailed proof of Shelah's result for graphs, and describe the extent of its generalizability to other sorts of structures. The extension axioms, which form the basis for earlier zero-one laws (for first-order logic, fixed-point logic, and finite-variable infinitary logic) are inadequate in the case of choiceless polynomial time; they must be replaced by what we call the strong extension axioms. We present an extensive discussion of these axioms and their role both in the zero-one law and in general.

Sign in / Sign up

Export Citation Format

Share Document