Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2105.02444

Parallelized sequential composition, pipelines, and hardware weak memory models

Robert J. Colvin
View original source ↗Read source document ↗Export metadata ↓

Abstract

Since the introduction of the CDC 6600 in 1965 and its `scoreboarding' technique processors have not (necessarily) executed instructions in program order. Programmers of high-level code may sequence independent instructions in arbitrary order, and it is a matter of significant programming abstraction and computational efficiency that the processor can be relied upon to make sensible parallelizations/reorderings of low-level instructions to take advantage of, eg., multiple ALUs. At the architectural level such reordering is typically implemented via a per-processor pipeline, into which instructions are fetched in order, but possibly committed out of order depending on local considerations, provided any reordering preserves sequential semantics from that processor's perspective. However multicore architectures, where several pipelines run in parallel, can expose these processor-level reorderings as unexpected, or `weak', behaviours. Such weak behaviours are hard to reason about, and (via speculative execution) underlie at least one class of widespread security vulnerability. In this paper we introduce a novel program operator, \emph{parallelized sequential composition}, which can be instantiated with a function that controls the reordering of atomic instructions. It generalises both sequential and parallel composition, and when appropriately instantiated exhibits many of the weak behaviours of well-known hardware weak memory models. Our framework admits the application of established compositional techniques (eg. Owicki-Gries) for reasoning about weak behaviours, and is convenient for abstractly expressing properties from the literature. The semantics and theory is encoded and verified in a theorem prover, and we give an implementation of the pipeline semantics which we use to empirically show conformance against established models of ARM and RISC-V.

Explore related subjects

cs.LO

Keep this discovery

BibTeXRIS

Robert J. Colvin. 2021-05-06. Parallelized sequential composition, pipelines, and hardware weak memory models. https://arxiv.org/abs/2105.02444

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A Four-Valued Graph Model for Conflict Resolution: Core Framework and a Machine-Checked Formalization in Lean 4

This note consolidates the core of the Quasi-Closed World Graph Model for Conflict Resolution (QCW-GMCR), which extends the standard Graph Model for Conflict Resolution with Belnap's four-valued logic to represent option-level epistemic ambiguity, and pairs the framework with a machine-checked Lean 4 formalization. QCW-GMCR combines: (1) FOUR-valued option assignments with compositional propagation to state-level feasibility; (2) graded reachability (definite, credible, possible) based on an FDE-inspired transition-warrant semantics, with definite reachability related to FDE consequence in the Boolean fragment; (3) axiomatized deterministic reductions from four-valued assessments to binary decisions, including four canonical operators reflecting distinct risk attitudes; and (4) catastrophe-avoiding equilibrium concepts with a quasi-closed-world safety invariant. A four-valued hypergame extension captures heterogeneous subjective assessments across decision makers. We state the core definitions and results and report the parts verified in Lean 4 with mathlib, including the classical GMCR stability hierarchy, algebraic and compositional properties of FOUR-valued conjunction, properties of the canonical reductions, and the graded reachability hierarchy. The formalization also helped identify and correct earlier claims, including a knowledge-monotonicity axiom replaced by truth monotonicity. This preprint provides a stable, citable record of the framework and its current formal verification status.

cs.LO↗
arXiv2026

The Semantic Elevation Operator and the Closure of the Undecidable Class under Preservation

The undecidability of a program's static semantic properties is governed by Rice's theorem. Self-modifying systems, however, require analysing not whether a property holds now, but whether it is preserved when the system rewrites itself. We formalise this transition through a semantic elevation operator {\Lambda}{\Phi}, which turns the static question "does x satisfy P?" into the dynamic question "is P preserved after x is transformed by {\Phi}?". We prove that when {\Phi} is intensional (depending on the source code, not only on the computed function), the elevated property remains undecidable even though it breaks the extensionality that Rice's theorem requires; the proof rests on Kleene's recursion theorem, not on Rice. Consequently the class U of non-verifiable properties is closed under the elevation operator. Unbounded iteration of the operator climbs the arithmetical hierarchy -to {\Pi}02-completeness- consolidating non-verifiability as a structural fact. We further show that the supervisory regress does not terminate: no fnite tower of increasingly capable verifiers yields an unconditional certificate. A categorical reading of these results in the efective topos, in which elevation appears as an instance of Lawvere's fxed-point theorem, is left as a direction for future work.

cs.LO↗
arXiv2026

Statistical Symmetry Release for Equivariant Quantum Learning

Hard symmetry constraints reduce model complexity, but can also erase label information. Statistical symmetry release determines when finite data and quantum measurements justify relaxing such a constraint, which directions to open, and how far to move. We connect global signal detection to local, loss-dependent improvement. A two-copy twirl--swap gate estimates task information in the symmetry-breaking complement with a dimension-independent copy count under paired-state and group-unitary access; reweighting the same records resolves representation sectors. An exact duality distinguishes this Hilbert--Schmidt signal from the larger signal accessible to bounded-outcome readouts. Local improvement is governed by the release gradient and a loss-corrected double-commutator matrix. Simultaneous confidence bounds convert empirical direction selection into certified descent, using either shared Pauli measurements or scalar probes with state-independent truncation bounds. Gaussian testing lower bounds quantify the cost of searching over unknown directions in the calibrated local experiment. Independent validation controls adaptively generated models, and a fast squared-loss bound preserves the approximation--estimation rate of a nested release path. On an eight-qubit Ising model, shared measurements certify release with 6300 times fewer shots than the specified scalar estimator on the tested budget grids. Quotient quantum natural gradient then controls parameter redundancy during training. Together, these results turn symmetry relaxation into a statistically justified model-selection decision.

cs.LO↗