Testing Theory of Truly Concurrent Processes

Yong Wang

arxiv: 2606.12944 · v1 · pith:EAC4UHM3new · submitted 2026-06-11 · 💻 cs.LO

Testing Theory of Truly Concurrent Processes

Yong Wang This is my paper

Pith reviewed 2026-06-27 05:42 UTC · model grok-4.3

classification 💻 cs.LO

keywords truly concurrent processestesting semanticsoperational semanticsaxiomatic semanticsdenotational semanticsprocess algebrastrue concurrencyHennessy's testing

0 comments

The pith

Truly concurrent processes admit testing semantics that inherit the operational-axiomatic-denotational trinity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops testing semantics for truly concurrent processes by adapting Hennessy's methods from interleaving concurrency. This approach ensures that the semantics includes operational, axiomatic, and denotational aspects. A reader would care because it connects models of true concurrency, such as Petri nets, with standard process calculi like CCS. The work aims to provide a unified way to reason about processes that execute actions concurrently rather than in interleaved steps.

Core claim

The paper establishes testing semantics for truly concurrent processes that follows Hennessy's approach and thereby provides operational semantics, axiomatic semantics, and denotational semantics for these processes.

What carries the argument

The adapted testing semantics that defines process equivalence based on the ability to pass or fail certain tests, extended to capture true concurrency behaviors.

If this is right

Operational semantics for truly concurrent processes can be defined through testing.
Algebraic axioms can be derived for the testing equivalence.
Denotational models can be constructed using the testing preorder.
This framework allows for the analysis of true concurrent systems using established techniques from interleaving concurrency.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The semantics could support direct transfer of testing-based verification methods to domains that require true concurrency.
It may reduce the practical gap between true concurrency and interleaving models when equivalence is defined by tests.
Alignment with specific models such as event structures could be checked by applying the same tests.

Load-bearing premise

The testing framework developed for interleaving concurrency can be directly adapted to truly concurrent processes while preserving the operational-axiomatic-denotational trinity.

What would settle it

A concrete truly concurrent process for which the adapted testing equivalence fails to match either its operational behavior, its algebraic axioms, or its denotational model would settle the claim.

Figures

Figures reproduced from arXiv: 2606.12944 by Yong Wang.

**Figure 1.** Figure 1: An example of fPAT branches. It is reasonable that all partial orders between actions in different parallel branches are communications. In the example of fPAT in fig. 1, there exist parallel branches denoted by ∥, alternative branches denoted by +, communications between parallel branches denoted by lines with arrows, and conflictions between parallel branches denoted by dashed lines. Communications and … view at source ↗

read the original abstract

A process is able to execute a set of actions with a predefined manner, while a truly concurrent process executes this set of actions with a manner with the flavour of true concurrency. The so-called truly concurrent process algebras bridge the true concurrency (such as Petri nets, event structures, etc), and the interleaving concurrency (such as CCS, CSP, ACP, etc). In this paper, we give truly concurrent processes testing semantics followed by Hennessy's great work, which inherits the trinity of operational semantics, axiomatic semantics and denotational semantics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The abstract claims an extension of testing semantics to true concurrency but provides no technical content to evaluate the claim.

read the letter

The main point here is that the paper says it has built testing semantics for truly concurrent processes that inherits the full operational-axiomatic-denotational trinity from Hennessy's interleaving work. That is the claim to check.

What is new is the direct move of testing theory into the true-concurrency setting, using models such as Petri nets and event structures instead of CCS-style interleaving. The motivation is stated plainly: a truly concurrent process executes a set of actions with genuine independence rather than sequential scheduling.

The paper does a reasonable job naming the gap it wants to close and citing the relevant prior work on testing.

The soft spot is that the abstract contains no definitions, no example derivations, no axioms, and no sketch of how the three semantics are shown to coincide. Without those pieces it is impossible to see whether the adaptation preserves the properties that made Hennessy's framework useful or whether new circularities appear when independence and causality are added. The assumption that the interleaving framework transfers with only minor changes therefore remains untested in the visible material.

This is a paper for people already working inside process algebra and true-concurrency models. A reader who follows that literature might get value once the full constructions are available, but the current text does not yet supply enough to judge the result.

I would bring the full paper to a reading group if the technical sections turn out to contain explicit rules and proofs. I would not cite it on the basis of the abstract alone.

The work shows straightforward engagement with the existing testing literature, so it counts as serious thinking on its own terms. It deserves a serious referee to examine whether the claimed inheritance actually holds once the definitions are written down.

Referee Report

1 major / 0 minor

Summary. The paper claims to develop testing semantics for truly concurrent processes by extending Hennessy's framework from interleaving concurrency, asserting that the resulting semantics inherits the trinity of operational, axiomatic, and denotational semantics.

Significance. If the inheritance of the trinity is demonstrated with explicit definitions and proofs, the work could bridge true-concurrency models (Petri nets, event structures) with interleaving models (CCS, CSP, ACP), extending classical testing theory in process algebra.

major comments (1)

[Abstract] Abstract: the claim that the testing semantics 'inherits the trinity of operational semantics, axiomatic semantics and denotational semantics' is asserted without any definitions, proofs, or examples, leaving the central claim without visible support or derivation steps.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and the constructive comment on the abstract. We address it point by point below.

read point-by-point responses

Referee: [Abstract] Abstract: the claim that the testing semantics 'inherits the trinity of operational semantics, axiomatic semantics and denotational semantics' is asserted without any definitions, proofs, or examples, leaving the central claim without visible support or derivation steps.

Authors: The abstract is a concise summary of the paper's main contribution. The full manuscript extends Hennessy's testing framework to truly concurrent process algebras by defining an operational testing semantics (via may- and must-testing preorders on processes), providing an axiomatic semantics (a sound and complete equational theory), and developing a corresponding denotational semantics (using event structures or similar truly concurrent models). We include proofs that the three semantics coincide, thereby inheriting the trinity. We will revise the abstract to make this structure explicit and to reference the sections where the definitions and proofs appear. revision: yes

Circularity Check

0 steps flagged

No circularity; direct adaptation of external Hennessy framework

full rationale

The paper states it gives testing semantics for truly concurrent processes 'followed by Hennessy's great work' and inherits the operational-axiomatic-denotational trinity. No equations, definitions, or claims in the provided material reduce any result to a self-fit, self-citation chain, or renaming of inputs. The central step is an explicit extension of an independent external source (Hennessy), with no load-bearing self-referential steps or uniqueness theorems imported from the authors' prior work. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; full manuscript required for audit.

pith-pipeline@v0.9.1-grok · 5598 in / 883 out tokens · 27648 ms · 2026-06-27T05:42:32.914673+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

16 extracted references · 3 canonical work pages

[1]

Wang, Algebraic theory for true concurrency, Elsevier AP, 2023

Y. Wang, Algebraic theory for true concurrency, Elsevier AP, 2023

2023
[2]

Wang, Handbook of truly concurrent process algebra, Elsevier MK, 2023

Y. Wang, Handbook of truly concurrent process algebra, Elsevier MK, 2023

2023
[3]

C. A. Petri, Non-sequential processes, GMD-ISF Report 77 (5) (1977)

1977
[4]

C. A. Petri, General net theory. communication disciplines, in: proc. Joint IBM University of Newcastle Seminar, B. Shaw ed., Newcastle GB, 1976

1976
[5]

C. A. Petri, Concurrency as a basis of systems thinking, in: Proc. from 5th Scandinavian Logic Symposium, 1979, pp. 143–162

1979
[6]

Winskel, Event structures, in: advanced course on Petri nets, Springer, 1986, pp

G. Winskel, Event structures, in: advanced course on Petri nets, Springer, 1986, pp. 325– 392

1986
[7]

Milner, A calculus of communicating systems, Springer, 1980

R. Milner, A calculus of communicating systems, Springer, 1980

1980
[8]

C. A. R. Hoare, Communicating sequential processes, Communications of the ACM 21 (8) (1978) 666–677. doi:10.1145/359576.359585

work page doi:10.1145/359576.359585 1978
[9]

C. A. R. Hoare, Communicating sequential processes, Prentice Hall International Series in Computer Science, Prentice-Hall, 1985

1985
[10]

Fokkink, Introduction to process algebra, 2nd Edition, Springer-Verlag, 2007

W. Fokkink, Introduction to process algebra, 2nd Edition, Springer-Verlag, 2007

2007
[11]

Hennessy, Algebraic theory of processes, Foundations of Computing, MIT Press, Cam- bridge, MA, 1988

M. Hennessy, Algebraic theory of processes, Foundations of Computing, MIT Press, Cam- bridge, MA, 1988

1988
[12]

Kapp´ e, Concurrent kleene algebra: completeness and decidability (doctoral dissertation, Ph.D

T. Kapp´ e, Concurrent kleene algebra: completeness and decidability (doctoral dissertation, Ph.D. thesis, UCL (University College London) (2020)

2020
[13]

Scott, C

D. Scott, C. Strachey, Towards a mathematical semantics for computer languages, in: J. Fox (Ed.), Proceedings of the Symposium on Computers and Automata, Vol. 21 of MRI Sym- posium Proceedings, Polytechnic Press, Brooklyn, New York, 1971, pp. 19–46

1971
[14]

J. A. Goguen, J. W. Thatcher, E. G. Wagner, J. B. Wright, Initial algebra semantics and continuous algebras, J. ACM 24 (1) (1977) 68–95. doi:10.1145/321992.321997

work page doi:10.1145/321992.321997 1977
[15]

Guessarian, Algebraic Semantics, Vol

I. Guessarian, Algebraic Semantics, Vol. 99 of Lecture Notes in Computer Science, Springer,
[16]

doi:10.1007/3-540-10284-7. 63

work page doi:10.1007/3-540-10284-7

[1] [1]

Wang, Algebraic theory for true concurrency, Elsevier AP, 2023

Y. Wang, Algebraic theory for true concurrency, Elsevier AP, 2023

2023

[2] [2]

Wang, Handbook of truly concurrent process algebra, Elsevier MK, 2023

Y. Wang, Handbook of truly concurrent process algebra, Elsevier MK, 2023

2023

[3] [3]

C. A. Petri, Non-sequential processes, GMD-ISF Report 77 (5) (1977)

1977

[4] [4]

C. A. Petri, General net theory. communication disciplines, in: proc. Joint IBM University of Newcastle Seminar, B. Shaw ed., Newcastle GB, 1976

1976

[5] [5]

C. A. Petri, Concurrency as a basis of systems thinking, in: Proc. from 5th Scandinavian Logic Symposium, 1979, pp. 143–162

1979

[6] [6]

Winskel, Event structures, in: advanced course on Petri nets, Springer, 1986, pp

G. Winskel, Event structures, in: advanced course on Petri nets, Springer, 1986, pp. 325– 392

1986

[7] [7]

Milner, A calculus of communicating systems, Springer, 1980

R. Milner, A calculus of communicating systems, Springer, 1980

1980

[8] [8]

C. A. R. Hoare, Communicating sequential processes, Communications of the ACM 21 (8) (1978) 666–677. doi:10.1145/359576.359585

work page doi:10.1145/359576.359585 1978

[9] [9]

C. A. R. Hoare, Communicating sequential processes, Prentice Hall International Series in Computer Science, Prentice-Hall, 1985

1985

[10] [10]

Fokkink, Introduction to process algebra, 2nd Edition, Springer-Verlag, 2007

W. Fokkink, Introduction to process algebra, 2nd Edition, Springer-Verlag, 2007

2007

[11] [11]

Hennessy, Algebraic theory of processes, Foundations of Computing, MIT Press, Cam- bridge, MA, 1988

M. Hennessy, Algebraic theory of processes, Foundations of Computing, MIT Press, Cam- bridge, MA, 1988

1988

[12] [12]

Kapp´ e, Concurrent kleene algebra: completeness and decidability (doctoral dissertation, Ph.D

T. Kapp´ e, Concurrent kleene algebra: completeness and decidability (doctoral dissertation, Ph.D. thesis, UCL (University College London) (2020)

2020

[13] [13]

Scott, C

D. Scott, C. Strachey, Towards a mathematical semantics for computer languages, in: J. Fox (Ed.), Proceedings of the Symposium on Computers and Automata, Vol. 21 of MRI Sym- posium Proceedings, Polytechnic Press, Brooklyn, New York, 1971, pp. 19–46

1971

[14] [14]

J. A. Goguen, J. W. Thatcher, E. G. Wagner, J. B. Wright, Initial algebra semantics and continuous algebras, J. ACM 24 (1) (1977) 68–95. doi:10.1145/321992.321997

work page doi:10.1145/321992.321997 1977

[15] [15]

Guessarian, Algebraic Semantics, Vol

I. Guessarian, Algebraic Semantics, Vol. 99 of Lecture Notes in Computer Science, Springer,

[16] [16]

doi:10.1007/3-540-10284-7. 63

work page doi:10.1007/3-540-10284-7