Termination Behavior Research Articles

Transformation techniques for context-sensitive rewrite systems

Context-sensitive rewriting is a computational restriction of term rewriting used to model non-strict (lazy) evaluation in functional programming. The goal of this paper is the study and development of techniques to analyze the termination behavior of context-sensitive rewrite systems. For that purpose, several methods have been proposed in the literature which transform context-sensitive rewrite systems into ordinary rewrite systems such that termination of the transformed ordinary system implies termination of the original context-sensitive system. In this way, the huge variety of existing techniques for termination analysis of ordinary rewriting can be used for context-sensitive rewriting, too. We analyze the existing transformation techniques for proving termination of context-sensitive rewriting and we suggest two new transformations. Our first method is simple, sound, and more powerful than the previously proposed transformations. However, it is not complete, i.e., there are terminating context-sensitive rewrite systems that are transformed into non-terminating term rewrite systems. The second method that we present in this paper is both sound and complete. All these observations also hold for rewriting modulo associativity and commutativity.

Chain Length Dependent Termination in Free Radical Copolymerization. 1. The Copolymerization System Styrene−Methyl Methacrylate in Bulk at 25 °C

The termination behavior in the stationary free radical copolymerization system styrene (ST)-methyl methacrylate (MMA) at 25 °C was reexamined by means of two newly developed methods. In essence, these are adaptations of the now already familiar methods of determining k t from rates and degrees of polymerization, originally developed for analysis of pulsed laser polymerization (PLP) experiments, for steady-state experiments conducted by photoinitiation using a continuous light source. Like the earlier methods they allow for the determination of the termination coefficient k t as a function of chain length. The extent of the chain length dependence of k t , characterized by the parameter b in the power law connecting k t and radical chain length v', k t = A(v') -b , is found to be on the order of 0.1 over the full composition range (including the two monomers ST and MMA) which is slightly smaller than the data obtained from PLP for the two pure monomers (0.16-0.18). However, there are no large variations as a function of feed composition. The absolute values of k t either obtained via extrapolation to unity chain lengths (k 1.1 t) or calculated for a fixed chain length of 500 (k 500 t), however, pass through a maximum. In view of the diffusion-controlled character of the termination reaction this result is interpreted by assuming the mobility of the chain ends to be increased when a monomer unit different from the terminal unit is incorporated into the penultimate (or penpenultimate) position of the growing chain, especially if MMA is replaced by ST in a MMA terminated chain. Assisted by the alternation tendency of the copolymer system ST-MMA this might finally lead to an overall chain end mobility in excess of that of either homopolymeric radical for intermediate monomer compositions.

Surface Termination and Thermal Elimination Behaviour of Activated Hydrogenated Germanium

AbstractActivated hydrogenated germanium that shows a high chemical reactivity for insertion into various non‐metal/non‐metal bonds, was investigated by surface IR spectroscopy with respect to its surface properties and potential elimination reactions at the surface. Spectroscopic and kinetic data stongly suggest that the high reactivity is due to intrinsic defects and dangling bonds in the amorphous network and does not stem from an elimination step prior to the insertion of the activated germanium. Further investigations support our former description of activated germanium as a low‐valent germanium hydride with a minor content of chloride. In addition, small amounts of coordinated 1, 4‐dioxane can be found on the surface.

Household Income, Termination Risk and Mortgage Pricing

The premium embedded in home mortgage loans to compensate investors for their exposure to prepayment risk is a significant component of the cost of home mortgage lending. Moreover, there is some reason to believe that prepayment risk may be lower for loans to lower-income housing borrowers, especially those that are first-time home owners. If so, investor recognition of this advantage should facilitate greater willingness to acquire portfolios of lower-income housing loans, and encourage more competitive pricing in this segment of the market. This study investigates the possibility of differential mortgage prepayment behavior between lower-income home owners and non-low income home owners. The investigation relies on samples of the American Housing Survey spanning ten years of experience from 1985 to 1995. We find no significant difference between the termination or refinancing behavior of non-low income and low-income households. This result is robust to a number of alternative specifications such as restricting the low-income test group to non-moving households and to first-time owners. The same conclusions are derived from both aggregate prepayment rates and from analysis of individual household prepayment behavior.

Context-Sensitive Rewriting Strategies

Context-sensitive rewriting is a simple rewriting restriction which is formalized by imposing fixed restrictions on replacements. Such a restriction is given on a purely syntactic basis: it is given on the arguments of symbols of the signature and inductively extended to arbitrary positions of terms built from those symbols. The termination behavior is not only preserved but usually improved and several methods have been developed to formally prove it. In this paper, we investigate the definition, properties, and use of context-sensitive rewriting strategies , i.e., particular, fixed sequences of context-sensitive rewriting steps. We study how to define them in order to obtain efficient computations and to ensure that context-sensitive computations terminate whenever possible. We give conditions enabling the use of these strategies for root-normalization, normalization, and infinitary normalization. We show that this theory is suitable for formalizing the definition and analysis of real computational strategies which are used in programming languages such as OBJ or ELAN.

Context-Sensitive Rewriting Strategies

Context-sensitive rewriting is a simple rewriting restriction which is formalized by imposing fixed restrictions on replacements. Such a restriction is given on a purely syntactic basis: it is given on the arguments of symbols of the signature and inductively extended to arbitrary positions of terms built from those symbols. The termination behavior is not only preserved but usually improved and several methods have been developed to formally prove it. In this paper, we investigate the definition, properties, and use of context-sensitive rewriting strategies , i.e., particular, fixed sequences of context-sensitive rewriting steps. We study how to define them in order to obtain efficient computations and to ensure that context-sensitive computations terminate whenever possible. We give conditions enabling the use of these strategies for root-normalization, normalization, and infinitary normalization. We show that this theory is suitable for formalizing the definition and analysis of real computational strategies which are used in programming languages such as OBJ or ELAN.

Lazy Rewriting and Context-Sensitive Rewriting

Lazy rewriting (LR) is intended to improve the termination behavior of TRSs. This is attempted by restricting reductions for selected arguments of functions. Similarly, context-sensitive rewriting (CSR) forbids any reduction on those arguments. We show that LR and CSR coincide under certain conditions. On the basis of this result, we also describe a transformation which permits us to prove termination of LR as termination of CSR for the transformed system. Since there are a number of different techniques for proving termination of CSR, this provides a formal framework for proving termination of lazy rewriting.

From checking to inference via driving and dag grammars

Abramov and Glück have recently introduced a technique called URA for inverting first order functional programs. Given some desired output value, URA computes a potentially infinite sequence of substitutions/restrictions corresponding to the relevant input values. In some cases this process does not terminate.In the present paper, we propose a new program analysis for inverting programs. The technique works by computing a finite grammar describing the set of all input that relate to a given output. During the production of the grammar, the original program is implicitly transformed using so-called driving steps. Whereas URA is sound and complete, but sometimes fails to terminate, our technique always terminates and is complete, but not sound. As an example, we demonstrate how to derive type inference from type checking.The idea of approximating functional programs by grammars is not new. For instance, the second author has developed a technique using tree grammars to approximate termination behaviour of deforestation. However, for the present purposes it has been necessary to invent a new type of grammar that extends tree grammars by permitting a notion of sharing in the productions. These dag grammars seem to be of independent interest.

Just-in-time: On Strategy Annotations

A simple kind of strategy annotations is investigated, giving rise to a class of strategies, including leftmost-innermost. It is shown that under certain restrictions on annotations, an interpreter can be written which computes a normal form of a term in a bottom-up traversal. The main contribution is a correctness proof of this interpreter. Furthermore, a default strategy annotation is provided, called just-in-time, which satisfies the criteria for the interpreter. The just-in-time strategy has a better termination behaviour than innermost rewriting for many interesting examples.

Using Changes in Initiation and Chain Transfer Rates To Probe the Kinetics of Cross-Linking Photopolymerizations: Effects of Chain Length Dependent Termination

The importance of incorporating chain length dependent termination (CLDT) behavior into the interpretation of the kinetics of cross-linked systems has been examined. Kinetic chain length distributions were varied in a variety of di(meth)acrylate photopolymerizations via the manipulation of the initiation rate and the chain transfer rate. Shifting the kinetic chain lengths toward shorter chains has little visible effect on multiacrylate systems. In contrast, similar changes in the corresponding multimethacrylate polymerizations changed the kinetics significantly. Shorter kinetic chains led to the delayed onset of reaction−diffusion-controlled termination behavior, as well as an increase in the ratio of kt/kp[M] at all conversions prior to the onset of reaction−diffusion control. Additionally, the magnitude of the kinetic constant ratio in the reaction−diffusion-controlled regime was affected by the kinetics at low conversion in the polymerization of a rubbery system, PEG(600)DMA. This behavior was independent of the method used to alter the kinetic chain length distribution and thus implies that CLDT may potentially impact the network formation in polymerizations occurring above the Tg of the system. These results illustrate that, although counterintuitive, CLDT is an important factor in cross-linking free radical polymerizations.

Lazy rewriting on eager machinery

The article introduces a novel notion of lazy rewriting. By annotating argument positions as lazy, redundant rewrite steps are avoided, and the termination behavior of a term-rewriting system can be improved. Some transformations of rewrite rules enable an implementation using the same primitives as an implementation of eager rewriting.

The Impact of Bank Consolidation on Commercial Borrower Welfare

We estimate the impact of bank merger announcements on borrowersâ stock prices for publicly traded Norwegian firms. In addition, we analyze how bank mergers influence borrower relationship termination behavior and relate the propensity to terminate to borrower abnormal returns. We obtain four main results. First, on average borrowers lose about 1 percent in equity value when their bank is announced as a merger target. Small borrowers of target banks are especially hurt in mergers between two large banks, where they lose an average of about 3 percent. Small target borrowers are not harmed, and appear to even gain, from mergers between small banks. Second, bank mergers lead to higher relationship exit rates for three years after a bank merger, and small bank mergers lead to larger increases in exit rates than large mergers. Third, target borrower abnormal returns are positively related to pre-merger exit rates, indicating that firms that find it easier to switch banks are less harmed when their bank merges. Fourth, we find weak evidence that target borrowers with large merger-induced increases in exit rates are more negatively affected by bank merger announcements, suggesting that target borrowers can be forced out of relationships and suffer welfare losses as a result of bank mergers.

Demographic versus Option-Driven Mortgage Terminations

This study examines mortgage termination behavior at the household level, including fixed-rate mortgage terminations due to call, default, and mobility behavior. It exploits information in the American Housing Survey to examine national cross sections of 6119 and 4160 owner households. While accounting for the influence of interest rate movements in motivating termination—the call option influence—the study uses two sequential panels to investigate the modifying effect of household financial, demographic, and location characteristics upon termination behavior. Although we find the effect of the call option (systematic effect) to be highly significant in explaining terminations in a declining interest rate environment, we also find that demographic and locational effects (diversifiable) are potentially at least as significant. This result suggests that incomplete diversification over the nonsystematic factors of demography and location could cause significant variation in termination rates.

Intrinsic termination of T7 RNA polymerase mediated by either RNA or DNA.

Intrinsic termination of T7 RNA polymerase transcription occurs at different signals in vitro. One type of signal is similar to that mediating factor-independent termination of Escherichia coli RNA polymerase, whereas the other type does not involve RNA hairpin formation. By examining the termination behaviour of T7 RNA polymerase at the E.coli rrnB operon t1 terminator, at the T7-t(phi) terminator, at the human preproparathyroid hormone gene terminator on both single- and double-stranded templates, and in the presence of GTP or ITP during transcription, we show that the termination event can be mediated by either RNA or DNA structural features. Moreover, by using co-transcriptional probing with potassium permanganate, we present evidence for the presence of transcription-induced hyperreactive thymidines on the non-template strand in the DNA-mediated event, and a putative sequence motif is identified. We conclude that intrinsic termination of T7 RNA polymerase transcription in vitro can be mediated either by a hairpin in the nascent RNA or by a sequence motif including hyperreactive thymidines in the non-template DNA strand.

Adolescents' reasoning about authority and friendship relations in the context of drug usage

Two studies were conducted on adolescents' reasoning about authority and friendship relations within the context of drug usage. One hundred and forty-five subjects were individually interviewed about questions pertaining to (a) the rights of parents to prohibit a friendship, (b) one's obligation to follow parental rules, (c) peers' active response to a friend's drug behavior, (d) ratings of rule importance and degree of wrongness, (e) friendship termination behavior, and (f) peer influence. The findings demonstrated that adolescents' evaluations of the authority and friendship questions were influenced by the drug type and the question posed. Younger adolescents, in comparison to their older peers, judged that parents have a right to regulate friendship behaviors and peers are obligated to obey the rules. The younger group also indicated that it would be all right to report to an authority a friend's drug use.

Mathematical foundations for time warp systems

We develop a simple formal model of the Time Warp approach to distributed computation, prove several important properties of the model, and devise some extensions to Time Warp that provide improved termination behavior. Our model consists of processes that communicate solely via message passing. One of the basic process steps is a rollback operation that includes message retraction via transmission of antimessages. In the model, we consider three problems: safety, progress, and termination. By safety, we mean that for a given system of processes, if a run of the system terminates, then the final system state of the run is identical to the final system state of a rollback-free run. We give premises that imply safety, and a counterexample that shows how safety can fail. By progress, we mean that, as a run of a system proceeds, the minimum timestamp of an unprocessed message always eventually increases. We state three axioms that imply the progress property. By termination, we mean that, if all rollback-free runs of a system terminate, then all runs terminate. The termination property is generally false in existing implementations of Time Warp systems due to the possibility of Time Warp vortices. We define additional mechanisms that can guarantee the termination property for most Time Warp applications.

Playfighting in Captive Red-Necked Wallabies, Macropus Rufogriseus Banksianus

The structure and development of playfighting in captive red-necked wallabies, Macropus rufogriseus banksianus, was studied over a 2.5 year period. An ethogram of 21 acts was established. Playfighting involved acts from agonistic, affiliative and sexual contexts. The sequential organisation of acts was highly non-random in both intra- and inter-individual structure. Sequence analysis grouped acts into 3 subsystems : those associated with high (central act: Spar) and low (central act: Paw) intensity bouts of fighting; and those associated with initiation, termination or interbout behaviour. Wallabies playfought at varying intensities ranging from high intensity Sparring matches to low intensity bouts of Pawing coupled with frequent and prolonged periods of affiliative interactions. A third type of playfighting, refusal playfights, was of short duration and was probably failed playfight initiations. There was considerable repetition of acts and sequences of acts, and play-partners interacted in a highly mutual manner. Some acts (Skip, side and chest Autogroom, and Shake) were performed in an apparently exaggerated manner and may have had a communicative function. There was noticable restraint used in the performance of Kicking during playfights compared to that seen in serious fights. The goal of playfighting was either to gain unrestricted grooming access to an opponent's throat or to force an opponent off-balance causing it to retreat. Males of any age playfought more often than females; playfighting in females was very rare. Wallabies engaged in playfights soon after they first began to leave their mother's pouch. Three phases of playfight development in males were identified. The first was an early phase of vigorous play that ended about the time wallabies were weaned. The second phase commenced after weaning and continued until after sexual maturity. It was a transitional period of increasing instability in playfight relations manifested as shorter playfights and more refusal playfights. The final phase was characterised by low intensity playfighting and was typical of older adult males. The design of playfighting and age/sex differences in its performance were used to consider the relative importance of motor training, socialisation and assessment of fighting skills as benefits of playfighting. Most evidence favours motor training as the most important benefit, particularly for high intensity playfighting. For low intensity playfights motor training was not completely satisfactory as the main benefit. It was possible that low intensity playfights gave a different type of motor training than high intensity playfights. Developmental changes in the type of playfighting performed also suggest that either the motor training benefits a wallaby required from play changes with age, or there were age-related changes in the function of playfighting. Neither socialisation or assessment of fighting skills seem to be major benefits of playfighting in the wallabies. The similarities between playfighting in the wallabies and play in better studied taxa (i.e. eutherians), and between wallaby playfighting and the descriptions given in the macropodid literature of prolonged, resource-unrelated serious fights are considered. It was concluded that at least some of the fights of macropodids reported in the literature were misclassed playfights.

Strong termination of logic programs

We study a powerful class of logic programs which terminate for a large class of goals. Both classes are characterized in a natural way in terms of mappings from variable-free atoms to natural numbers. We present a technique based on this idea which improves the termination behavior and allows a more multidirectional use of Prolog programs. The class of logic programs is shown to be strong enough to compute every total recursive function. The class of goals considerably extends the variable-free ones.

The Relative Termination Experience of Adjustable to Fixed‐Rate Mortgages

ABSTRACTOur study uses a multinomial logit model to analyze the concurrent termination experience of adjustable‐rate and fixed‐rate mortgages. A new set of ARM‐specific interactive determinants expands the conventional FRM specification to isolate the unique termination behavior of ARMs. We find that expected rate adjustments and large lifetime caps are positively related to ARM termination probabilities while long adjustment frequencies are inversely related. Caps, both periodic and lifetime, have a secondary, inverse effect on termination probabilities when interest‐rate movements exceed cap limits. The model also shows that interest‐rate expectations affect FRM terminations more strongly than ARM terminations.

Simulation and design of lossy transmission lines in a thin-film multichip package

A thin-film multichip package design was evaluated for its applications in packaging high-performance VLSI/ULSI chips. Typical thin-film interconnections (copper lines 8 mu m wide and 4 mu m thick) were analyzed, and a large CMOS driver was used in the simulation. It was found that a pitch of 32 mu m for the microstrip configuration and 20 mu m for the stripline configuration is required to obtain a low-crosstalk environment for an input frequency up to 1 GHz. It is shown that long lines (length between 8 cm and 18 cm) do not need any termination, but short lines (shorter than 8 cm, but longer than the length at which a line is considered to be a lumped circuit) must be terminated with customized termination resistors to obtain optimal package performance. The loading effects n the termination behavior of short and long thin-film microstrips are also discussed. It is shown that high power generation in thin-film lines at a high frequency (1 GHz) would require an advanced cooling technique for the thin-film multichip package. >