Termination Of Loops Research Articles

TERMINATION ANALYSIS OF LINEAR LOOPS

Verification of program termination is an important problem in program correctness analysis. Automatically proving termination or finding nonterminating inputs as counter-examples for many programs will be a big breakthrough in theoretical computer science. A remarkable result, provided by Tiwari(2004), showed that the termination of linear loops is decidable and an eventually nonterminating input can be found for the given nonterminating loop. But some essential lemmas were missing in that proof and his algorithm could not generate a nonterminating input, which might be more widely utilized in software testing. In this paper, we discuss these details carefully and present an algorithm for producing a nonterminating input automatically. We reduce the problem of finding a nonterminating input to that of computing real root bound of a multi-exponential polynomial. This algorithm has been implemented in a Maple package based on symbolic computation. Thereby a stronger and complete decidable result in termination problem is established.

From program verification to program synthesis

This paper describes a novel technique for the synthesis of imperative programs. Automated program synthesis has the potential to make programming and the design of systems easier by allowing programs to be specified at a higher-level than executable code. In our approach, which we call proof-theoretic synthesis, the user provides an input-output functional specification, a description of the atomic operations in the programming language, and a specification of the synthesized program's looping structure, allowed stack space, and bound on usage of certain operations. Our technique synthesizes a program, if there exists one, that meets the input-output specification and uses only the given resources. The insight behind our approach is to interpret program synthesis as generalized program verification, which allows us to bring verification tools and techniques to program synthesis. Our synthesis algorithm works by creating a program with unknown statements, guards, inductive invariants, and ranking functions. It then generates constraints that relate the unknowns and enforces three kinds of requirements: partial correctness, loop termination, and well-formedness conditions on program guards. We formalize the requirements that program verification tools must meet to solve these constraint and use tools from prior work as our synthesizers. We demonstrate the feasibility of the proposed approach by synthesizing programs in three different domains: arithmetic, sorting, and dynamic programming. Using verification tools that we previously built in the VS3 project we are able to synthesize programs for complicated arithmetic algorithms including Strassen's matrix multiplication and Bresenham's line drawing; several sorting algorithms; and several dynamic programming algorithms. For these programs, the median time for synthesis is 14 seconds, and the ratio of synthesis to verification time ranges between 1x to 92x (with an median of 7x), illustrating the potential of the approach.

Proving loop termination: Beyond the traditional method

The traditional method for proving loop termination requires us to define a bound function of program variables. The criterion in this method is well-defined and can be easy to apply, as such functions are obvious for many loops. However in some cases, it can be very difficult to define a bound function. In this paper, we discuss how to prove loop termination by using alternative methods. First we show how to prove loop termination by solving a recursive relation that defines the number of iterations remaining in any execution state. Then we introduce a step-by-step approach for applying this recursive relation method. This new method can also be used to investigate preconditions that lead to loop termination in non-deterministic cases. Finally, we illustrate another method that uses a more general criterion for proving loop termination. The new criterion is a generalization of the classical one. This paper does not attempt to offer a one-size-fits-all approach. Rather, it provides some alternative methods that make proving loop termination easier in some cases, where termination might otherwise be difficult if not impossible to prove.

Lightning Transients in Low-Voltage Installations Inside Different Types of Class II Lightning Protection Systems

This paper presents a numerical electromagnetic analysis of loop-termination voltages inside an outer lightning protection system (LPS) resulting from direct and indirect lightning strikes. The method of moments is combined with the transmission-line model and employed to model the whole structure in three dimensions and the lightning channel, respectively. Three distinct types of class II LPS are modeled with one- and three single-phase parallel vertical loops of the TN-S system inside the LPS. All cases are simulated by using the negative subsequent stroke current with linear-rising front at lightning-protection level II. The connected equipment at the loop terminals is considered in the offstate to simulate the worst condition. The results reveal that for the three-loop configurations, the middle-loop termination voltages of all floors are always higher than those of the outer loops and the frequency of oscillations of the middle loop is roughly twice that of the outer ones. In addition, the midedge strike case gives higher loop-termination voltages for all floors than those of the corner strike case. For the slender LPS, the effect of the strike location dominates in the case of high surge impedance of the feeder only.

Contracts for concurrency

AbstractThe SCOOP model extends the Eiffel programming language to provide support for concurrent programming. The model is based on the principles of Design by Contract. The semantics of contracts used in the original proposal (SCOOP_97) is not suitable for concurrent programming because it restricts parallelism and complicates reasoning about program correctness. This article outlines a new contract semantics which applies equally well in concurrent and sequential contexts and permits a flexible use of contracts for specifying the mutual rights and obligations of clients and suppliers while preserving the potential for parallelism. We argue that it is indeed a generalisation of the traditional correctness semantics. We also propose a proof technique for concurrent programs which supports proofs—similar to those for traditional non-concurrent programs—of partial correctness and loop termination in the presence of asynchrony.

A Ringed Non-Uniform Network: How to Raise its Efficiency

A Ringed Non-Uniform Network: How to Raise its Efficiency As distinct from radial electric power lines, in closed loops the consumers are fed from two sides. This is advantageous from the viewpoint of supply reliability, power quality and its losses; however, these are the least only when a loop is uniform, which is not always met in practice. In a non-uniform loop a circulating current flows, and the losses increase proportionally to its square. To reduce losses in such a non-uniform loop, the circulating current should be eliminated. For this purpose a booster transformer can be used. The voltage of such a transformer is known to be in quadrature to the phase voltage; the present consideration has shown that such orientation of the opposing voltage gives the best results only when all loads in the loop are active, otherwise the angle of opposing voltage should be regulated. The voltage value should also be regulated depending on the load. Another technique consists in introducing a complementary reactance into the terminal branches. Such reactance should be regulated if loads are changing in time disproportionately with respect to each other. The best results are achieved when all loop node loads have the same cosφ. If the complementary reactance calculated at one end of the loop is positive, then that calculated at the second end of the loop will be negative, and vice versa. The appropriate choice can be made, in particular, involving both loop terminals.

Mutual coupling of two collocated orthogonally oriented circular thin-wire loops

Coupling between two collocated orthogonal circular thin-wire loops is analyzed in this paper. Two coupled integral equations for the loop currents are derived and their solution in general form is found in terms of Fourier series. An analytical expression for currents induced through the mutual coupling is obtained for the case when all loop current harmonics higher than first can be ignored. It is found that strong coupling can exist for all loop current harmonics, except for the fundamental. It is also found that coupling for orthogonal collocated loop antennas depends on the relative locations of the loop terminals.

A practical run-time technique for exploiting loop-level parallelism

In order to exploit potential parallelism of loops, in which the array access patterns cannot be analyzed at compile-time, parallelizing compilers must rely on the run-time dependence analysis techniques. The LRPD test is noted in this field for its applicability. It assumes full parallelism and executes speculatively, then examines the correctness of parallel execution after loop termination. We extended the concept and developed a practical run-time technique, called the speculative parallelization with new technology (SPNT) test, to further exploit loop-level parallelism. Two main characteristics make the SPNT test distinguished. The first is improving the success rate of speculative parallelization by eliminating all cross-iteration data dependences except the cross-processor flow dependences. The second is reducing the failure penalty by aborting the speculative parallel execution immediately once a cross-processor flow dependence is detected during the execution. Our experimental results on shared-memory parallel machines HP SPP2000 and ALR QUAD6 prove the high effectiveness of the SPNT test.

Sulfite:Cytochrome c Oxidoreductase fromThiobacillus novellus: PURIFICATION, CHARACTERIZATION, AND MOLECULAR BIOLOGY OF A HETERODIMERIC MEMBER OF THE SULFITE OXIDASE FAMILY

Direct oxidation of sulfite to sulfate occurs in various photo- and chemotrophic sulfur oxidizing microorganisms as the final step in the oxidation of reduced sulfur compounds and is catalyzed by sulfite:cytochrome c oxidoreductase (EC ). Here we show that the enzyme from Thiobacillus novellus is a periplasmically located alphabeta heterodimer, consisting of a 40.6-kDa subunit containing a molybdenum cofactor and an 8.8-kDa mono-heme cytochrome c(552) subunit (midpoint redox potential, E(m8.0) = +280 mV). The organic component of the molybdenum cofactor was identified as molybdopterin contained in a 1:1 ratio to the Mo content of the enzyme. Electron paramagnetic resonance spectroscopy revealed the presence of a sulfite-inducible Mo(V) signal characteristic of sulfite:acceptor oxidoreductases. However, pH-dependent changes in the electron paramagnetic resonance signal were not detected. Kinetic studies showed that the enzyme exhibits a ping-pong mechanism involving two reactive sites. K(m) values for sulfite and cytochrome c(550) were determined to be 27 and 4 micrometer, respectively; the enzyme was found to be reversibly inhibited by sulfate and various buffer ions. The sorAB genes, which encode the enzyme, appear to form an operon, which is preceded by a putative extracytoplasmic function-type promoter and contains a hairpin loop termination structure downstream of sorB. While SorA exhibits significant similarities to known sequences of eukaryotic and bacterial sulfite:acceptor oxidoreductases, SorB does not appear to be closely related to any known c-type cytochromes.

Circus movement atrial flutter in canine sterile pericarditis model. Activation patterns during entrainment and termination of single-loop reentry in vivo.

Recently, we used a custom designed "jacket" electrode with 127 bipolar electrodes in a flexible nylon matrix to map the total atrial epicardial surface in the in situ canine heart. Atrial flutter in dogs with sterile pericarditis was shown to be due to a single wave front circulating around a combined functional/anatomic obstacle, with the arc of functional conduction block contiguous with one or more of the atrial vessels. In the present study, this model was used to analyze the activation pattern during pacing-induced entrainment and termination of single reentrant loops in a syncytium without anatomically predetermined pathways. Sustained atrial flutter was induced in five dogs with 3-5-day-old sterile pericarditis. Atrial pacing at a cycle length 5-30 msec shorter than the spontaneous cycle length entrained the arrhythmia and could result in a "classical" activation pattern, characterized by an antidromic stimulated wave that collided with the reentrant orthodromic wave front of the previous beat at a constant site. However, two variations of this classical activation pattern were also observed: 1) Pacing at short cycle lengths could lead to localized conduction block in antidromic direction, forcing a change in the pathway of the antidromic wave front. This could prevent the expected shift of the site of collision in antidromic direction. 2) The stimulated orthodromic wave front could also use a pathway different from that of the original reentrant impulse, so that a different circuit was active during the pacing period. Termination of atrial flutter by rapid atrial stimulation was associated with progressive slowing and finally blocking of the paced orthodromic wave front and a progressive shift of the site of collision in antidromic direction. The occurrence of conduction block was determined by the cycle length of stimulation and the number of stimulated beats. A longer train at the critical cycle length or the critical number of beats at a shorter cycle length could reinduce the same reentrant circuit or a different reentrant circuit, respectively, during stimulated cycles following the beat that terminated reentry. The epicardial activation sequence during entrainment of reentrant arrhythmias does not necessarily follow a standard activation pattern. Instead, the stimulated orthodromic as well as the antidromic wave front might use a pathway different from that of the original reentrant wave front. The mechanisms of termination, failure of termination, and reinitiation of single-loop reentry are similar to those in the "figure-eight" reentrant circuit.

The pursuit of deadlock freedom

We introduce some combinatorial techniques for establishing the deadlock freedom of concurrent systems which are similar to the variant/invariant method of proving loop termination. Our methods are based on the local analysis of networks, which is combinatorially far easier than analysing all global states. They are illustrated by proving numerous examples to be free of deadlock, some of which are useful classes of network.

Some ramifications of the EXIT statement in loop control

EXIT statements support a style of programming that distinguishes between the control operations and the actions in a loop. Readability suggests that multiple EXIT statements are preferable to a single EXIT statement in a loop with multiple invariants. This is particularly true if implementational considerations have confused the neatness of the loop termination condition.

Forced termination of loops

AbstractLoops must often be forced to terminate early. Solutions to such problems are usually either language‐dependent or rather clumsy. A practical alternative is presented. The accompanying methodology clarifies the role of the finalization mechanism in loop construction. It also leads to the idea of control‐structure independence in the context of data representation and forced termination.

Some Properties Derived from Structural Analysis of Program Graph Models

It is considered interesting to identify, from the structure of control flow and of relationships among variables in a program, some properties allowing to point out possible sources of errors or of faulty behavior. In particular, it is found that information about termination of loops and about meaningfulness of acceptance tests in recopery block strategy can be extracted from such structural analysis. Criteria for applying this analysis to programs with arbitrary structures are presented.

A Proof System for Communicating Sequential Processes

An axiomatic proof system is presented for proving partial correctness and absence of deadlock (and failure) of communicating sequential processes. The key (meta) rule introduces cooperation between proofs, a new concept needed to deal with proofs about synchronization by message passing. CSP's new convention for distributed termination of loops is dealt with. Applications of the method involve correctness proofs for two algorithms, one for distributed partitioning of sets, the other for distributed computation of the greatest common divisor of n numbers.