[Paper Review] About Instruction Sequence Testing

J.A. Bergstra|arXiv (Cornell University)|Jan 18, 2012

Software Testing and Debugging Techniques24 references3 citations

TL;DR

This paper proposes developing a formal theory of instruction sequence testing (polinseq testing) as a foundational model for software testing, using polyadic instruction sequences as a minimal computational abstraction. By focusing on precise operational semantics, performance metrics, and fault detection through execution, it aims to provide a stable, mathematically grounded framework that avoids the conceptual ambiguity of traditional software testing.

ABSTRACT

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.

Motivation & Objective

• To address the lack of a coherent, unified theoretical framework for software testing, which remains fragmented across competing definitions and perspectives.
• To propose instruction sequence testing (specifically polinseq testing) as a new, minimalistic theoretical model that can serve as a prototype for broader software testing theory.
• To overcome the conceptual confusion in existing software testing definitions by grounding testing in executable, formal instruction sequences with precise semantics.
• To establish a stable, mathematically formalizable framework for testing that is independent of programming language trends or implementation artifacts.
• To explore whether a theory of polinseq testing can serve as a viable model for program testing, offering clarity and precision where current approaches lack.

Proposed method

• Using polyadic instruction sequences (polinseqs) as a minimal, formal representation of programs, abstracting away from conventional programming syntax.
• Defining testing as the execution of a polinseq with the goal of detecting faults, grounded in operational semantics and performance constraints.
• Introducing precise performance notions such as maximal internal delay and bounded-step execution to model real-world testing constraints.
• Combining projection semantics and operational semantics to define clear cause-effect relationships between faults and observable failures.
• Developing a two-phase approach: first engaging in 'naive polinseq testing' to gain practical intuition, then refining definitions based on that experience.
• Formalizing testing concepts in a mathematical style without reliance on existing programming notations, ensuring theoretical stability and abstraction from syntactic trends.

Experimental results

Research questions

• RQ1 Can a formal theory of instruction sequence testing be developed that serves as a coherent model for software testing, despite the absence of a unified definition in the broader field?
• RQ2 How can performance metrics like maximal internal delay and bounded execution steps be formally defined and integrated into a testing framework for instruction sequences?
• RQ3 To what extent can a theory of polinseq testing provide a stable, mathematically grounded alternative to the current fragmented and context-dependent definitions of software testing?
• RQ4 Is it both legitimate and beneficial to develop theoretical definitions of polinseq testing before gaining hands-on experience in naive testing, or is practical experience a necessary prerequisite?
• RQ5 How can the operational and projection semantics of polinseqs be combined to precisely model fault detection and failure causality in testing?

Key findings

• A theory of instruction sequence testing (polinseq testing) can be developed as a foundational model for software testing, offering a formal, mathematically stable alternative to the current conceptual chaos in the field.
• Precise performance notions such as maximal internal delay and bounded-step execution can be formally defined and implemented within the polinseq framework, enabling low-level performance testing.
• The combination of projection semantics and operational semantics allows for a clear, operational meaning of each polinseq, facilitating precise analysis of fault-failure relationships.
• Naive polinseq testing—practical experimentation without a prior theoretical framework—is not only legitimate but potentially valuable as a preparatory step toward formal definition.
• The paper concludes that while a formal theory of polinseq testing is both possible and advisable, it should be informed by practical experience, though not necessarily dependent on it.
• The proposed framework avoids reliance on programming language syntax, making it resilient to shifts in programming paradigms and ensuring long-term theoretical stability.