arXiv subjects

J. A. Bergstra

Publications and source records attributed to J. A. Bergstra.

At least 37 records · Page 2Linked to original sources

arXiv2014

Informatics Perspectives on Decision Taking, a Case Study on Resolving Process Product Ambiguity

A decision is an act or event of decision taking. Decision making always includes decision taking, the latter not involving significant exchanges with non-deciding agents. A decision outcome is a piece of storable information constituting the result of a decision. Decision outcomes are typed, for instance: plan, command, assertion, or boolean reply to a question. Decision outcomes are seen by an audience and autonomous actions from the audience is supposed to realize the putting into effect of a decision outcome, thus leading to so-called decision effects. Decision outcomes are supposedly expected by the decider. Using a model or a theory concerning the causal chain leading from a decision outcome to one or more decision effects may support a decision taker decision taker in predicting plausible decision effects for candidate decision outcomes. Decision taking is positioned amidst many related notions including: decision making, decision process, decision making process, decision process making, decision engineering, decision progression, and decision progression production.

cs.OH↗

arXiv2014

Division by zero in non-involutive meadows

Meadows have been proposed as alternatives for fields with a purely equational axiomatization. At the basis of meadows lies the decision to make the multiplicative inverse operation total by imposing that the multiplicative inverse of zero is zero. Thus, the multiplicative inverse operation of a meadow is an involution. In this paper, we study `non-involutive meadows', i.e.\ variants of meadows in which the multiplicative inverse of zero is not zero, and pay special attention to non-involutive meadows in which the multiplicative inverse of zero is one.

math.RA↗

arXiv2014

Long multiplication by instruction sequences with backward jump instructions

For each function on bit strings, its restriction to bit strings of any given length can be computed by a finite instruction sequence that contains only instructions to set and get the content of Boolean registers, forward jump instructions, and a termination instruction. Backward jump instructions are not necessary for this, but instruction sequences can be significantly shorter with them. We take the function on bit strings that models the multiplication of natural numbers on their representation in the binary number system to demonstrate this by means of a concrete example. The example is reason to discuss points concerning the halting problem and the concept of an algorithm.

cs.PL↗

arXiv2013

Timed tuplix calculus and the Wesseling and van den Bergh equation

We develop an algebraic framework for the description and analysis of financial behaviours, that is, behaviours that consist of transferring certain amounts of money at planned times. To a large extent, analysis of financial products amounts to analysis of such behaviours. We formalize the cumulative interest compliant conservation requirement for financial products proposed by Wesseling and van den Bergh by an equation in the framework developed and define a notion of financial product behaviour using this formalization. We also present some properties of financial product behaviours. The development of the framework has been influenced by previous work on the process algebra ACP.

q-fin.GN↗

arXiv2013

Instruction sequence based non-uniform complexity classes

We present an approach to non-uniform complexity in which single-pass instruction sequences play a key part, and answer various questions that arise from this approach. We introduce several kinds of non-uniform complexity classes. One kind includes a counterpart of the well-known non-uniform complexity class P/poly and another kind includes a counterpart of the well-known non-uniform complexity class NP/poly. Moreover, we introduce a general notion of completeness for the non-uniform complexity classes of the latter kind. We also formulate a counterpart of the well-known complexity theoretic conjecture that NP is not included in P/poly. We think that the presented approach opens up an additional way of investigating issues concerning non-uniform complexity.

cs.CC↗

arXiv2013

Data linkage algebra, data linkage dynamics, and priority rewriting

We introduce an algebra of data linkages. Data linkages are intended for modelling the states of computations in which dynamic data structures are involved. We present a simple model of computation in which states of computations are modelled as data linkages and state changes take place by means of certain actions. We describe the state changes and replies that result from performing those actions by means of a term rewriting system with rule priorities. The model in question is an upgrade of molecular dynamics. The upgrading is mainly concerned with the features to deal with values and the features to reclaim garbage.

cs.LO↗

arXiv2013

A process calculus with finitary comprehended terms

We introduce the notion of an ACP process algebra and the notion of a meadow enriched ACP process algebra. The former notion originates from the models of the axiom system ACP. The latter notion is a simple generalization of the former notion to processes in which data are involved, the mathematical structure of data being a meadow. Moreover, for all associative operators from the signature of meadow enriched ACP process algebras that are not of an auxiliary nature, we introduce variable-binding operators as generalizations. These variable-binding operators, which give rise to comprehended terms, have the property that they can always be eliminated. Thus, we obtain a process calculus whose terms can be interpreted in all meadow enriched ACP process algebras. Use of the variable-binding operators can have a major impact on the size of terms.

cs.LO↗

arXiv2013

Network algebra for synchronous dataflow

We develop an algebraic theory of synchronous dataflow networks. First, a basic algebraic theory of networks, called BNA (Basic Network Algebra), is introduced. This theory captures the basic algebraic properties of networks. For synchronous dataflow networks, it is subsequently extended with additional constants for the branching connections that occur between the cells of synchronous dataflow networks and axioms for these additional constants. We also give two models of the resulting theory, the one based on stream transformers and the other based on processes as considered in process algebra.

cs.LO↗

arXiv2012

Indirect jumps improve instruction sequence performance

Instruction sequences with direct and indirect jump instructions are as expressive as instruction sequences with direct jump instructions only. We show that, in the case where the number of instructions is not bounded, we are faced with increases of the maximal internal delays of instruction sequences on execution that are not bounded by a linear function if we strive for acceptable increases of the lengths of instruction sequences on elimination of indirect jump instructions.

cs.PL↗

arXiv2012

On the behaviours produced by instruction sequences under execution

We study several aspects of the behaviours produced by instruction sequences under execution in the setting of the algebraic theory of processes known as ACP. We use ACP to describe the behaviours produced by instruction sequences under execution and to describe two protocols implementing these behaviours in the case where the processing of instructions takes place remotely. We also show that all finite-state behaviours considered in ACP can be produced by instruction sequences under execution.

cs.PL↗

arXiv2012

Process algebra with conditionals in the presence of epsilon

In a previous paper, we presented several extensions of ACP with conditional expressions, including one with a retrospection operator on conditions to allow for looking back on conditions under which preceding actions have been performed. In this paper, we add a constant for a process that is only capable of terminating successfully to those extensions of ACP, which can be very useful in applications. It happens that in all cases the addition of this constant is unproblematic.

cs.LO↗

arXiv2012

Instruction sequence processing operators

Instruction sequence is a key concept in practice, but it has as yet not come prominently into the picture in theoretical circles. This paper concerns instruction sequences, the behaviours produced by them under execution, the interaction between these behaviours and components of the execution environment, and two issues relating to computability theory. Positioning Turing's result regarding the undecidability of the halting problem as a result about programs rather than machines, and taking instruction sequences as programs, we analyse the autosolvability requirement that a program of a certain kind must solve the halting problem for all programs of that kind. We present novel results concerning this autosolvability requirement. The analysis is streamlined by using the notion of a functional unit, which is an abstract state-based model of a machine. In the case where the behaviours exhibited by a component of an execution environment can be viewed as the behaviours of a machine in its different states, the behaviours concerned are completely determined by a functional unit. The above-mentioned analysis involves functional units whose possible states represent the possible contents of the tapes of Turing machines with a particular tape alphabet. We also investigate functional units whose possible states are the natural numbers. This investigation yields a novel computability result, viz. the existence of a universal computable functional unit for natural numbers.

cs.LO↗

arXiv2012

Turing Impossibility Properties for Stack Machine Programming

The strong, intermediate, and weak Turing impossibility properties are introduced. Some facts concerning Turing impossibility for stack machine programming are trivially adapted from previous work. Several intriguing questions are raised about the Turing impossibility properties concerning different method interfaces for stack machine programming.

cs.LO↗

arXiv2012

About Instruction Sequence Testing

Software testing is presented as a so-called theme within which different authors and groups have defined different subjects each of these subjects having a different focus on testing. A uniform concept of software testing is non-existent and the space of possible coherent perspectives on software testing, each fitting within the theme, is viewed as being spanned by five dimensions, each dimension representing two opposite views with a variety of intermediate views in between. Instruction sequences are used as a simple theoretical conceptualization of computer programs. A theory of instruction sequence testing may serve as a model for a theory of software testing. Instruction sequences testing is considered a new topic for which definitions may be freely contemplated without being restricted by existing views on software testing. The problem of developing a theory of instruction sequence testing is posed. A survey is given of motivations and scenarios for developing a theory of instruction sequence testing.

cs.SE↗

arXiv2011

Stratified Outsourcing Theory

The terminology of sourcing, outsourcing and insourcing is developed in detail on the basis of the preliminary definitions of outsourcing and insourcing and related activities and competences as given in our three previous papers on business mereology, on the concept of a sourcement, and on outsourcing competence respectively. Besides providing more a detailed semantic analysis we will introduce, explain, and illustrate a number of additional concepts including: principal unit of a sourcement, theme of a sourcement, current sourcement, (un)stable sourcement, and sourcement transformation. A three level terminology is designed: (i) factual level: operational facts that hold for sourcements including histories thereof, (ii) business level: roles and objectives of various parts of the factual level description, thus explaining each partner's business process and business objectives, (iii) contract level: specification of intended facts and intended business models as found at the business level. Orthogonal to these three conceptual levels, are four temporal aspects: history, now (actuality), transformation, and transition. A detailed description of the well-known range of sourcement transformations is given.

cs.SE↗

arXiv2011

Outsourcing Competence

The topic of this paper, competences needed for outsourcing, is organized by first providing a generic competence scheme, which is subsequently instantiated to the area of sourcing and outsourcing. Sourcing and outsourcing are positioned as different areas of activity, neither one of which is subsumed under the other one. It is argued that competences relevant for outsourcing are mainly community based rather than evidence based. Subjective ability and objective ability are distinguished as categories, together making up ability, which are distinct but not necessarily disjoint from competence. Conjectural ability is introduced as a form of subjective ability. A person's competence profile includes competences as well as abilities, including subjective ones. Competence assessment and acquisition as well as the impact of assessed competence on practical work is described. The analysis of competence and ability thus developed is used as standpoint from which to extract a specification of an audience for a theory of outsourcing, yet to be written. Moreover, it allows to formulate requirements for and in preparation of the development of an outsourcing theory. Formulating these requirements is done under the assumption that a person's awareness of a theory of outsourcing is expected to strengthen that person's outsourcing competence profile.

cs.OH↗

arXiv2011

Introducing Sourcements

Sourcing processes are discussed at a high abstraction level. A dedicated terminology is developed concerning general aspects of sourcing. The term sourcement is coined to denote a building block for sourcing. No- tions of allocation, functional architecture and allocational architecture, equilibrium, and configuration are discussed. Limitations of the concept of outsourcing are outlined. This theoretical work is meant to serve as a point of departure for the subsequent development of a detailed theory of sourcing and sourcing transformations, which can be a tool for dealing with practical applica- tions.

cs.SE↗

arXiv2011

Interest prohibition and financial product innovation

We give a rough sketch of the Judaic, Greek, Islamic and Christian positions in the matter of interest prohibition during the last few millennia and discuss the way in which interest prohibition is dealt with in Islamic finance, the problems with authority-based arguments for interest prohibition, and the prospects of interest prohibition with the advent of electronic money.

q-fin.GN↗