Inversive Meadows and Divisive Meadows

Inversive meadows are commutative rings with a multiplicative identity element and a total multiplicative inverse operation whose value at 0 is 0. Divisive meadows are inversive meadows with the multiplicative inverse operation replaced by a division operation. We give finite equational specifications of the class of all inversive meadows and the class of all divisive meadows. It depends on the angle from which they are viewed whether inversive meadows or divisive meadows must be considered more basic. We show that inversive and divisive meadows of rational numbers can be obtained as initial algebras of finite equational specifications. In the spirit of Peacock's arithmetical algebra, we study variants of inversive and divisive meadows without an additive identity element and/or an additive inverse operation. We propose simple constructions of variants of inversive and divisive meadows with a partial multiplicative inverse or division operation from inversive and divisive meadows. Divisive meadows are more basic if these variants are considered as well. We give a simple account of how mathematicians deal with 1 / 0, in which meadows and a customary convention among mathematicians play prominent parts, and we make plausible that a convincing account, starting from the popular computer science viewpoint that 1 / 0 is undefined, by means of some logic of partial functions is not attainable.Comment: 18 pages; error corrected; 29 pages, combined with arXiv:0909.2088 [math.RA] and arXiv:0909.5271 [math.RA

A thread calculus with molecular dynamics

We present a theory of threads, interleaving of threads, and interaction between threads and services with features of molecular dynamics, a model of computation that bears on computations in which dynamic data structures are involved. Threads can interact with services of which the states consist of structured data objects and computations take place by means of actions which may change the structure of the data objects. The features introduced include restriction of the scope of names used in threads to refer to data objects. Because that feature makes it troublesome to provide a model based on structural operational semantics and bisimulation, we construct a projective limit model for the theory.Comment: 47 pages; examples and results added, phrasing improved, references replace

Is One Hyperparameter Optimizer Enough?

Hyperparameter tuning is the black art of automatically finding a good combination of control parameters for a data miner. While widely applied in empirical Software Engineering, there has not been much discussion on which hyperparameter tuner is best for software analytics. To address this gap in the literature, this paper applied a range of hyperparameter optimizers (grid search, random search, differential evolution, and Bayesian optimization) to defect prediction problem. Surprisingly, no hyperparameter optimizer was observed to be `best' and, for one of the two evaluation measures studied here (F-measure), hyperparameter optimization, in 50\% cases, was no better than using default configurations. We conclude that hyperparameter optimization is more nuanced than previously believed. While such optimization can certainly lead to large improvements in the performance of classifiers used in software analytics, it remains to be seen which specific optimizers should be applied to a new dataset.Comment: 7 pages, 2 columns, accepted for SWAN1

An interface group for process components

We take a process component as a pair of an interface and a behaviour. We study the composition of interacting process components in the setting of process algebra. We formalize the interfaces of interacting process components by means of an interface group. An interesting feature of the interface group is that it allows for distinguishing between expectations and promises in interfaces of process components. This distinction comes into play in case components with both client and server behaviour are involved.Comment: 26 pages; section on non-associativity of component composition added, examples adde

Decision Taking for Selling Thread Startup

Decision Taking is discussed in the context of the role it may play for a selling agent in a search market, in particular for agents involved in the sale of valuable and relatively unique items, such as a dwelling, a second hand car, or a second hand recreational vessel. Detailed connections are made between the architecture of decision making processes and a sample of software technology based concepts including instruction sequences, multi-threading, and thread algebra. Ample attention is paid to the initialization or startup of a thread dedicated to achieving a given objective, and to corresponding decision taking. As an application, the selling of an item is taken as an objective to be achieved by running a thread that was designed for that purpose

Program algebra with a jump-shift instruction

We study sequential programs that are instruction sequences with jump-shift instructions in the setting of PGA (ProGram Algebra). Jump-shift instructions preceding a jump instruction increase the position to jump to. The jump-shift instruction is not found in programming practice. Its merit is that the expressive power of PGA extended with the jump-shift instruction, is not reduced if the reach of jump instructions is bounded. This is used to show that there exists a finite-state execution mechanism that by making use of a counter can produce each finite-state thread from some program that is a finite or periodic infinite sequence of instructions from a finite set.Comment: 19 page

Dialectical Roots for Interest Prohibition Theory

It is argued that arguments for strict prohibition of interests must be based on the use of arguments from authority. This is carried out by first making a survey of so-called dialectical roots for interest prohibition and then demonstrating that for at least one important positive interest bearing financial product, the savings account with interest, its prohibition cannot be inferred from a match with any of these root cases

Meadow enriched ACP process algebras

We introduce the notion of an ACP process algebra. The models of the axiom system ACP are the origin of this notion. ACP process algebras have to do with processes in which no data are involved. We also introduce the notion of a meadow enriched ACP process algebra, which is a simple generalization of the notion of an ACP process algebra to processes in which data are involved. In meadow enriched ACP process algebras, the mathematical structure for data is a meadow.Comment: 8 pages; correction in Table

Instruction sequences for the production of processes

Single-pass instruction sequences under execution are considered to produce behaviours to be controlled by some execution environment. Threads as considered in thread algebra model such behaviours: upon each action performed by a thread, a reply from its execution environment determines how the thread proceeds. Threads in turn can be looked upon as producing processes as considered in process algebra. We show that, by apposite choice of basic instructions, all processes that can only be in a finite number of states can be produced by single-pass instruction sequences.Comment: 23 pages; acknowledgement corrected, reference update