arXiv subjects

C. A. Middelburg

Publications and source records attributed to C. A. Middelburg.

At least 73 records · Page 4Linked to original sources

arXiv2010

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.

math.RA↗

arXiv2010

Functional units for natural numbers

Interaction with services provided by an execution environment forms part of the behaviours exhibited by instruction sequences under execution. Mechanisms related to the kind of interaction in question have been proposed in the setting of thread algebra. Like thread, service is an abstract behavioural concept. The concept of a functional unit is similar to the concept of a service, but more concrete. A state space is inherent in the concept of a functional unit, whereas it is not inherent in the concept of a service. In this paper, we establish the existence of a universal computable functional unit for natural numbers and related results.

cs.PL↗

arXiv2010

Autosolvability of halting problem instances for instruction sequences

We position Turing's result regarding the undecidability of the halting problem as a result about programs rather than machines. The mere requirement that a program of a certain kind must solve the halting problem for all programs of that kind leads to a contradiction in the case of a recent unsolvability result regarding the halting problem for programs. In this paper, we investigate this autosolvability requirement in a setting in which programs take the form of instruction sequences.

cs.LO↗

arXiv2010

Searching publications on software testing

This note concerns a search for publications in which the pragmatic concept of a test as conducted in the practice of software testing is formalized, a theory about software testing based on such a formalization is presented or it is demonstrated on the basis of such a theory that there are solid grounds to test software in cases where in principle other forms of analysis could be used. This note reports on the way in which the search has been carried out and the main outcomes of the search. The message of the note is that the fundamentals of software testing are not yet complete in some respects.

cs.SE↗

arXiv2010

Instruction sequences and non-uniform complexity theory

We develop theory concerning non-uniform complexity in a setting in which the notion of single-pass instruction sequence considered in program algebra is the central notion. We define counterparts of the complexity classes P/poly and NP/poly and formulate a counterpart of the complexity theoretic conjecture that NP is not included in P/poly. In addition, we define a notion of completeness for the counterpart of NP/poly using a non-uniform reducibility relation and formulate complexity hypotheses which concern restrictions on the instruction sequences used for computation. We think that the theory developed opens up an additional way of investigating issues concerning non-uniform complexity.

cs.CC↗

arXiv2010

On the definition of a theoretical concept of an operating system

We dwell on how a definition of a theoretical concept of an operating system, suitable to be incorporated in a mathematical theory of operating systems, could look like. This is considered a valuable preparation for the development of a mathematical theory of operating systems.

cs.OS↗

arXiv2010

Data linkage dynamics with shedding

We study shedding in the setting of data linkage dynamics, a simple model of computation that bears on the use of dynamic data structures in programming. Shedding is complementary to garbage collection. With shedding, each time a link to a data object is updated by a program, it is determined whether or not the link will possibly be used once again by the program, and if not the link is automatically removed. Thus, everything is made garbage as soon as it can be viewed as garbage. By that, the effectiveness of garbage collection becomes maximal.

cs.LO↗

arXiv2010

Searching publications on operating systems

This note concerns a search for publications in which one can find statements that explain the concept of an operating system, reasons for introducing operating systems, a formalization of the concept of an operating system or theory about operating systems based on such a formalization. It reports on the way in which the search has been carried out and the outcome of the search. The outcome includes not only what the search was meant for, but also some added bonuses.

cs.OS↗

arXiv2009

Partial Komori fields and imperative Komori fields

This paper is concerned with the status of 1/0 and ways to deal with it. These matters are treated in the setting of Komori fields, also known as non-trivial cancellation meadows. Different viewpoints on the status of 1/0 exist in mathematics and theoretical computer science. We give a simple account of how mathematicians deal with 1/0 in which a customary convention among mathematicians plays a prominent part, 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.

math.RA↗

arXiv2009

Instruction sequences with dynamically instantiated instructions

We study sequential programs that are instruction sequences with dynamically instantiated instructions. We define the meaning of such programs in two different ways. In either case, we give a translation by which each program with dynamically instantiated instructions is turned into a program without them that exhibits on execution the same behaviour by interaction with some service. The complexity of the translations differ considerably, whereas the services concerned are equally simple. However, the service concerned in the case of the simpler translation is far more powerful than the service concerned in the other case.

cs.PL↗

arXiv2009

Thread extraction for polyadic instruction sequences

In this paper, we study the phenomenon that instruction sequences are split into fragments which somehow produce a joint behaviour. In order to bring this phenomenon better into the picture, we formalize a simple mechanism by which several instruction sequence fragments can produce a joint behaviour. We also show that, even in the case of this simple mechanism, it is a non-trivial matter to explain by means of a translation into a single instruction sequence what takes place on execution of a collection of instruction sequence fragments.

cs.PL↗

arXiv2009

A protocol for instruction stream processing

The behaviour produced by an instruction sequence under execution is a behaviour to be controlled by some execution environment: each step performed actuates the processing of an instruction by the execution environment and a reply returned at completion of the processing determines how the behaviour proceeds. In this paper, we are concerned with the case where the processing takes place remotely. We describe a protocol to deal with the case where the behaviour produced by an instruction sequence under execution leads to the generation of a stream of instructions to be processed and a remote execution unit handles the processing of that stream of instructions.

cs.PL↗

arXiv2009

Machine structure oriented control code logic

Control code is a concept that is closely related to a frequently occurring practitioner's view on what is a program: code that is capable of controlling the behaviour of some machine. We present a logical approach to explain issues concerning control codes that are independent of the details of the behaviours that are controlled. Using this approach, such issues can be explained at a very abstract level. We illustrate this among other things by means of an example about the production of a new compiler from an existing one. The approach is based on abstract machine models, called machine structures. We introduce a model of systems that provide execution environments for the executable codes of machine structures and use it to go into portability of control codes.

cs.SE↗

arXiv2009

Transmission protocols for instruction streams

Threads as considered in thread algebra model behaviours to be controlled by some execution environment: upon each action performed by a thread, a reply from its execution environment -- which takes the action as an instruction to be processed -- determines how the thread proceeds. In this paper, we are concerned with the case where the execution environment is remote: we describe and analyse some transmission protocols for passing instructions from a thread to a remote execution environment.

cs.PL↗

arXiv2009

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.

math.RA↗

arXiv2009

On the expressiveness of single-pass instruction sequences

We perceive programs as single-pass instruction sequences. A single-pass instruction sequence under execution is considered to produce a behaviour to be controlled by some execution environment. Threads as considered in basic thread algebra model such behaviours. We show that all regular threads, i.e. threads that can only be in a finite number of states, can be produced by single-pass instruction sequences without jump instructions if use can be made of Boolean registers. We also show that, in the case where goto instructions are used instead of jump instructions, a bound to the number of labels restricts the expressiveness.

cs.PL↗

arXiv2008

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.

cs.LO↗

arXiv2008

On the operating unit size of load/store architectures

We introduce a strict version of the concept of a load/store instruction set architecture in the setting of Maurer machines. We take the view that transformations on the states of a Maurer machine are achieved by applying threads as considered in thread algebra to the Maurer machine. We study how the transformations on the states of the main memory of a strict load/store instruction set architecture that can be achieved by applying threads depend on the operating unit size, the cardinality of the instruction set, and the maximal number of states of the threads.

cs.AR↗