# f

Published articles for f.

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## Complexity of conjunctive regular path query homomorphisms

DevFeed: [Complexity of conjunctive regular path query homomorphisms](<https://devfeed.tech/articles/complexity-of-conjunctive-regular-path-query-homomorphisms-115952.md>)

Original publisher: [Read original article](<https://arxiv.org/abs/2305.07271>)

Author: Laurent Beaudou, Florent Foucaud, Florent R. Madelaine, Lhouari Nourine, Anantha Padmanabha, Ga\\'etan Richad

Published: 2026-11-04T05:00:00Z

Content type: article

Language: en

Sources: [arXiv: Databases](<https://devfeed.tech/sources/arxiv-databases.md>)

Topics: [graph-database](<https://devfeed.tech/topics/graph-database.md>), [computational complexity](<https://devfeed.tech/topics/computational-complexity.md>), [Regular expression](<https://devfeed.tech/topics/regular-expression.md>), [polynomials](<https://devfeed.tech/topics/polynomials.md>)

Tags: [abstract](<https://devfeed.tech/tags/abstract.md>), [algorithm](<https://devfeed.tech/tags/algorithm.md>), [alphabet](<https://devfeed.tech/tags/alphabet.md>), [also](<https://devfeed.tech/tags/also.md>), [applications](<https://devfeed.tech/tags/applications.md>), [arc](<https://devfeed.tech/tags/arc.md>), [arxiv](<https://devfeed.tech/tags/arxiv.md>), [based](<https://devfeed.tech/tags/based.md>), [can](<https://devfeed.tech/tags/can.md>), [cases](<https://devfeed.tech/tags/cases.md>), [complete](<https://devfeed.tech/tags/complete.md>), [complexity](<https://devfeed.tech/tags/complexity.md>), [cs-db](<https://devfeed.tech/tags/cs-db.md>), [cs-dm](<https://devfeed.tech/tags/cs-dm.md>), [cs-fl](<https://devfeed.tech/tags/cs-fl.md>), [cs-lo](<https://devfeed.tech/tags/cs-lo.md>), [database](<https://devfeed.tech/tags/database.md>), [databases](<https://devfeed.tech/tags/databases.md>), [extend](<https://devfeed.tech/tags/extend.md>), [f](<https://devfeed.tech/tags/f.md>), [fixed](<https://devfeed.tech/tags/fixed.md>), [form](<https://devfeed.tech/tags/form.md>), [query](<https://devfeed.tech/tags/query.md>), [regular](<https://devfeed.tech/tags/regular.md>)

### AI overview

The paper studies whether one regular graph pattern (RGP) has a navigational homomorphism to another, a homomorphism-based form of conjunctive regular path query (CRPQ) containment. With general walks, the problem is solvable in EXPSPACE. Restricting witnesses to simple paths or trails yields PSPACE-completeness. For restricted RGPs over a unary alphabet, the problem is in NP, and the authors identify certain cases that are solvable in polynomial time; the excerpt does not specify which cases.

### Source excerpt

arXiv:2305.07271v2 Announce Type: replace Abstract: A graph database is a digraph whose arcs are labeled with symbols from a fixed alphabet. A regular graph pattern (RGP) is a digraph whose arcs are labeled with regular expressions over the alphabet. RGPs model navigational queries for graph databases called \emph{conjunctive regular path queries} (CRPQs). A match of a CRPQ in the database is witnessed by a special navigational homomorphism of the corresponding RGP to the database, where vertices of the RGP are mapped by a function $f$ to the vertices of the database, and for each arc $uv$ of the RGP, we require the existence of a walk in the database from $f(u)$ to $f(v)$, such that the word corresponding to the sequence of labels of that walk belongs to the regular language labeling the arc $uv$. We extend this definition to one of navigational homomorphisms between two RGPs, modeling a homomorphism-based form of CRPQ containment. We study the complexity of deciding the existence of such a homomorphism between RGPs. We show that this problem, in the case where general walks are considered, can still be solved by an EXPSPACE algorithm (just like general CRPQ Containment, which is known to be EXPSPACE-complete). In the case of simple paths or trails, in fact the navigational homomorphism problem considered here becomes much more tractable, as it is PSPACE-complete. We also study the problem for restricted RGPs over a unary alphabet, that arise from some applications like XPath or SPARQL. For this case, homomorphism-based CRPQ containment is in NP. We prove that certain interesting cases are in fact polynomial-time solvable.

## Learning Kolmogorov Backward Operators for Spectral Analysis and Forecasting: A Data-Driven Variational Galerkin Framework

DevFeed: [Learning Kolmogorov Backward Operators for Spectral Analysis and Forecasting: A Data-Driven Variational Galerkin Framework](<https://devfeed.tech/articles/learning-kolmogorov-backward-operators-for-spectral-analysis-and-forecasting-a-data-driven-variational-galerkin-framework-108824.md>)

Original publisher: [Read original article](<https://arxiv.org/abs/2610.39580>)

Author: Yuanchao Xu, Claire Valva, Ben Gao, Isao Ishikawa

Published: 2026-10-30T04:00:00Z

Content type: article

Language: en

Sources: [arXiv: Machine Learning](<https://devfeed.tech/sources/arxiv-machine-learning.md>)

Topics: [Machine learning](<https://devfeed.tech/topics/machine-learning.md>), [Neural Network](<https://devfeed.tech/topics/neural-network.md>), [Predictive AI](<https://devfeed.tech/topics/predictive-ai.md>)

Tags: [abstract](<https://devfeed.tech/tags/abstract.md>), [analysis](<https://devfeed.tech/tags/analysis.md>), [approximation](<https://devfeed.tech/tags/approximation.md>), [arxiv](<https://devfeed.tech/tags/arxiv.md>), [cluster](<https://devfeed.tech/tags/cluster.md>), [comparison](<https://devfeed.tech/tags/comparison.md>), [compress](<https://devfeed.tech/tags/compress.md>), [cs-lg](<https://devfeed.tech/tags/cs-lg.md>), [data](<https://devfeed.tech/tags/data.md>), [data-driven](<https://devfeed.tech/tags/data-driven.md>), [error](<https://devfeed.tech/tags/error.md>), [estimator](<https://devfeed.tech/tags/estimator.md>), [experiments](<https://devfeed.tech/tags/experiments.md>), [f](<https://devfeed.tech/tags/f.md>), [factor](<https://devfeed.tech/tags/factor.md>), [fewer](<https://devfeed.tech/tags/fewer.md>), [first](<https://devfeed.tech/tags/first.md>), [forecasting](<https://devfeed.tech/tags/forecasting.md>), [framework](<https://devfeed.tech/tags/framework.md>), [learning](<https://devfeed.tech/tags/learning.md>), [math-ds](<https://devfeed.tech/tags/math-ds.md>), [operators](<https://devfeed.tech/tags/operators.md>)

### AI overview

The framework learns a fixed-lag Kolmogorov backward operator directly from data, then compresses its Galerkin projection onto an observable space chosen in advance or variationally. Its error analysis connects estimator learning error, sampling error in Galerkin inner products, and properties of the observable space to spectral estimates and forecasts. Near an isolated spectral cluster, the subspace's invariance defect controls its distance from the target invariant subspace. Forecast error depends on reduced-model one-step error and observable projection error; under stated invariant-measure, constant-preservation, and mean-zero stability conditions, the bound is uniform over forecast horizons. For deterministic dynamics, an FNO learning rate supplies one explicit learning-error bound. Experiments illustrate spectral approximation and long-rollout forecasting, and compare with EDMD when transition pairs are fewer than basis functions.

### Source excerpt

arXiv:2610.39580v1 Announce Type: cross Abstract: For a time-homogeneous Markov process, the fixed-lag solution operator \( (T_\tau f)(x)=\mathbb E[f(X_{t+\tau})\mid X_t=x] \) of the Kolmogorov backward equation evolves observables linearly and deterministically, even when the dynamics are stochastic. We approximate this operator using a two-stage method where we first approximate this operator directly from data, without knowledge of the governing equation (e.g., Fourier Neural Operator), and then compress the Galerkin projection onto a finite-dimensional observable space that is fixed in advance or selected variationally. The error analysis traces the learning error of the estimator, the sampling error of the Galerkin inner products, and the invariance and reconstruction properties of the observable space to the computed spectra and forecasts. The sampling error enters only through a multiplicative factor. Near an isolated spectral cluster, the invariance defect of a subspace controls its distance from the target invariant subspace. The forecast error is controlled by the one-step error of the reduced model and the projection error of the observable; when the measure is invariant and the reduced model preserves constants and is stable on mean-zero observables, the bound is uniform in the horizon. For deterministic dynamics, a learning rate for Fourier neural operators (FNOs) gives one explicit bound for the learning error. Numerical experiments illustrate spectral approximation and forecasting, including long-rollout stability and a comparison with extended dynamic mode decomposition (EDMD) when fewer transition pairs than basis functions are observed.

## Hidden-State Privacy Has an Empty Middle

DevFeed: [Hidden-State Privacy Has an Empty Middle](<https://devfeed.tech/articles/hidden-state-privacy-has-an-empty-middle-102968.md>)

Original publisher: [Read original article](<https://arxiv.org/abs/2605.24042>)

Author: Alexander Okezue Bell

Published: 2026-10-28T04:00:00Z

Content type: article

Language: en

Sources: [arXiv: Artificial Intelligence](<https://devfeed.tech/sources/arxiv-artificial-intelligence.md>), [arXiv: Machine Learning](<https://devfeed.tech/sources/arxiv-machine-learning.md>)

Topics: [Security & Privacy](<https://devfeed.tech/topics/security-privacy.md>), [LLM security](<https://devfeed.tech/topics/llm-security.md>), [Language models](<https://devfeed.tech/topics/language-models.md>)

Tags: [2](<https://devfeed.tech/tags/2.md>), [3](<https://devfeed.tech/tags/3.md>), [abstract](<https://devfeed.tech/tags/abstract.md>), [adaptive](<https://devfeed.tech/tags/adaptive.md>), [architecture](<https://devfeed.tech/tags/architecture.md>), [arxiv](<https://devfeed.tech/tags/arxiv.md>), [budget](<https://devfeed.tech/tags/budget.md>), [but](<https://devfeed.tech/tags/but.md>), [class](<https://devfeed.tech/tags/class.md>), [co-design](<https://devfeed.tech/tags/co-design.md>), [cs-ai](<https://devfeed.tech/tags/cs-ai.md>), [cs-lg](<https://devfeed.tech/tags/cs-lg.md>), [d](<https://devfeed.tech/tags/d.md>), [design](<https://devfeed.tech/tags/design.md>), [edge](<https://devfeed.tech/tags/edge.md>), [f](<https://devfeed.tech/tags/f.md>), [first](<https://devfeed.tech/tags/first.md>), [fixed](<https://devfeed.tech/tags/fixed.md>), [full](<https://devfeed.tech/tags/full.md>), [hidden](<https://devfeed.tech/tags/hidden.md>), [privacy](<https://devfeed.tech/tags/privacy.md>), [state](<https://devfeed.tech/tags/state.md>)

### AI overview

Among 1,536 tested Gaussian covariances for single-layer hidden-state release, none achieved both moderate utility and privacy against an adaptive retrieval attacker. A Fisher-ball lower bound further shows that every full-rank Gaussian release with O(1) Fisher utility has a direction whose Mahalanobis signal grows linearly with hidden width. The diagonal inverse-Fisher mechanism is uniquely minimax-optimal among diagonal releases at the stated first-order KL budget and alone kept worst-attacker top-1 at or below 0.001 across a 32 model-layer grid, but it lies at a privacy/utility edge. A generalized-eigen mechanism's 13x Pareto reduction under Euclidean retrieval vanished under adaptive Mahalanobis retrieval, where it reached 100% top-1. The abstract also reports that a split-memory transformer trained from scratch outperformed same-budget GPT baselines on its stated privacy measure, with a language-modeling loss penalty; it frames architecture or release co-design as a direction beyond Gaussian mechanism design. These are abstract-level claims; the supplied text notes that v4 was withdrawn.

### Source excerpt

arXiv:2605.24042v4 Announce Type: replace-cross Abstract: Of $1{,}536$ Gaussian release covariances we tested for single-layer hidden-state privacy, zero achieve both moderate utility and moderate privacy against an adaptive retrieval attacker. We prove a complementary Fisher-ball lower bound: every full-rank Gaussian release at $O(1)$ Fisher utility admits a direction whose Mahalanobis signal grows linearly in hidden width, ruling out uniform Gaussian safety in the class and matching the empirical empty middle. The diagonal inverse-Fisher release $\Sigma^\star_{\mathrm{diag}}(\mathcal{K}) = (2\mathcal{K}/d)\,\mathrm{diag}(1/F_{ii})$ is the unique minimax-optimal diagonal mechanism at first-order KL budget $\mathcal{K}$ and the only release with worst-attacker top-1 $\le 0.001$ at every point of a 32 model-layer grid, but it sits on a privacy/utility edge rather than filling the middle. A generalized-eigen mechanism reaching $13\times$ Pareto reduction under Euclidean retrieval collapses to $100\%$ top-1 under the adaptive Mahalanobis attacker, and a full-trajectory sequence inverter recovers $94\%$ of clean GPT-2 prefixes but $0\%$ under $\Sigma_{\mathrm{diag}}$. A split-memory transformer trained from scratch reaches $G_{\mathrm{Mah}} \in [20, 33]$ at 90M and maintains a $6$--$24\times$ advantage over same-budget GPT baselines from 30M to 1B at a fixed-token language-modeling loss penalty; pretrained models top out at 9.3. These results reframe hidden-state release from mechanism-design within the Gaussian class to architecture or release co-design.

## Collective Dynamics of Self-Reinforcement: How Cross-Task Coupling Drives Policy Collapse in Unsupervised RLVR

DevFeed: [Collective Dynamics of Self-Reinforcement: How Cross-Task Coupling Drives Policy Collapse in Unsupervised RLVR](<https://devfeed.tech/articles/collective-dynamics-of-self-reinforcement-how-cross-task-coupling-drives-policy-collapse-in-unsupervised-rlvr-104100.md>)

Original publisher: [Read original article](<https://arxiv.org/abs/2610.37553>)

Author: Peize Ding

Published: 2026-10-28T04:00:00Z

Content type: article

Language: en

Sources: [arXiv: Machine Learning](<https://devfeed.tech/sources/arxiv-machine-learning.md>)

Topics: [rlvr](<https://devfeed.tech/topics/rlvr.md>), [llm-reasoning](<https://devfeed.tech/topics/llm-reasoning.md>), [Reinforcement learning](<https://devfeed.tech/topics/reinforcement-learning.md>), [scaling laws](<https://devfeed.tech/topics/scaling-laws.md>)

Tags: [2](<https://devfeed.tech/tags/2.md>), [about](<https://devfeed.tech/tags/about.md>), [abstract](<https://devfeed.tech/tags/abstract.md>), [arxiv](<https://devfeed.tech/tags/arxiv.md>), [base](<https://devfeed.tech/tags/base.md>), [batch](<https://devfeed.tech/tags/batch.md>), [but](<https://devfeed.tech/tags/but.md>), [collective](<https://devfeed.tech/tags/collective.md>), [confidence](<https://devfeed.tech/tags/confidence.md>), [coupling](<https://devfeed.tech/tags/coupling.md>), [critical](<https://devfeed.tech/tags/critical.md>), [cross](<https://devfeed.tech/tags/cross.md>), [cs-lg](<https://devfeed.tech/tags/cs-lg.md>), [dataset](<https://devfeed.tech/tags/dataset.md>), [delta](<https://devfeed.tech/tags/delta.md>), [entropy](<https://devfeed.tech/tags/entropy.md>), [explain](<https://devfeed.tech/tags/explain.md>), [f](<https://devfeed.tech/tags/f.md>), [falls](<https://devfeed.tech/tags/falls.md>), [policy](<https://devfeed.tech/tags/policy.md>), [rlvr](<https://devfeed.tech/tags/rlvr.md>)

### AI overview

In label-free RLVR, rewarding a language model for agreeing with its own majority vote can initially improve reasoning but later drive self-assessed reward toward one while accuracy falls, sometimes to identical answers across problems. The paper models this as a collective instability: shared parameters amplify perturbations while problems remain uncertain, with growth tied to coupling strength, while per-problem sharpening slows as the number of training problems increases. The model predicts a critical dataset size that decreases with stronger coupling and higher initial uncertainty; simulations report a sharp transition and no collapse for confident initial models. A kernel analysis identifies protective coupling and a marginal-entropy bonus. In small-Transformer experiments, removing the shared direction prevents collapse, restoring it brings collapse back, and collapse increases with training-set size and base-model entropy.

### Source excerpt

arXiv:2610.37553v1 Announce Type: new Abstract: Label-free reinforcement learning with verifiable rewards (RLVR) rewards a language model for agreeing with its own majority vote. It improves reasoning at first but eventually collapses: the self-assessed reward goes to one while accuracy falls, often until the model gives the same answer to every problem. The collapse appears only when training uses many problems. We explain this dataset-size dependence as a collective instability. In a solvable many-problem model in which problems share parameters, a population whose problems prefer different answers amplifies any shared perturbation for as long as the population-averaged slope $\langle F'\rangle$ of the single-problem self-reinforcement drift $F$ is positive. This holds while problems are still uncertain about their answers. Per-problem sharpening, slowed by $1/N$ for $N$ training problems, races against the shared mode, which grows at a rate $\propto\lambda^2$ independent of $N$, where $\lambda$ is the strength of the shared coupling. This yields a critical number of problems $N_c\simeq\ln(1/\delta)/(\lambda^2G)$, where $\delta$ seeds the shared mode and $G$ decreases with the initial confidence. Simulations of the model confirm the predictions: a sharp transition, $N_c\propto\lambda^{-2}$ up to a logarithmic correction, a single critical amplification $\lambda^2NG$ across couplings, confidence profiles and training variants, a logarithmic dependence on batch size, and no collapse for confident initial models. A kernel version of the theory identifies a protective coupling (generalization of sharpening) and a marginal-entropy bonus that stabilizes the uniform collective mode. In label-free RL of a small Transformer, removing the shared direction prevents collapse entirely, restoring it causes collapse, and collapse grows with training-set size and base-model entropy.

## A Guide to Modern Python String Formatting Tools

DevFeed: [A Guide to Modern Python String Formatting Tools](<https://devfeed.tech/articles/a-guide-to-modern-python-string-formatting-tools-98859.md>)

Original publisher: [Read original article](<https://realpython.com/python-formatted-output/>)

Author: Leodanis Pozo Ramos

Published: 2026-10-24T14:00:00Z

Content type: tutorial

Language: en

Sources: [Real Python](<https://devfeed.tech/sources/real-python.md>)

Topics: [formatting](<https://devfeed.tech/topics/formatting.md>), [Python](<https://devfeed.tech/topics/python.md>), [Learning](<https://devfeed.tech/topics/learning.md>)

Tags: [align](<https://devfeed.tech/tags/align.md>), [alignment](<https://devfeed.tech/tags/alignment.md>), [argument](<https://devfeed.tech/tags/argument.md>), [arguments](<https://devfeed.tech/tags/arguments.md>), [arithmetic](<https://devfeed.tech/tags/arithmetic.md>), [automatic](<https://devfeed.tech/tags/automatic.md>), [base](<https://devfeed.tech/tags/base.md>), [bnf](<https://devfeed.tech/tags/bnf.md>), [boolean](<https://devfeed.tech/tags/boolean.md>), [built-in](<https://devfeed.tech/tags/built-in.md>), [class](<https://devfeed.tech/tags/class.md>), [component](<https://devfeed.tech/tags/component.md>), [f](<https://devfeed.tech/tags/f.md>), [format](<https://devfeed.tech/tags/format.md>), [formatting](<https://devfeed.tech/tags/formatting.md>), [modern](<https://devfeed.tech/tags/modern.md>), [python](<https://devfeed.tech/tags/python.md>), [string](<https://devfeed.tech/tags/string.md>), [strings](<https://devfeed.tech/tags/strings.md>), [tools](<https://devfeed.tech/tags/tools.md>)

### AI overview

The excerpt recommends f-strings for quick string formatting in modern Python: prefix a string with `f` or `F` and put variables or expressions in curly-brace fields. Values are interpolated when the f-string runs, so referenced names must already be defined. The `.format()` method fills fields in a template from positional or named arguments, which the excerpt identifies as useful for older Python versions or legacy code. Its positional fields may be numbered or automatically sequenced, but those numbering styles cannot be mixed; missing fields or arguments can raise errors. Both tools support conversions such as `!s` and `!r` and format specifications for type, width, alignment, fill, sign, precision, and digit grouping. The excerpt also notes that Python 3.12 expanded f-string expression capabilities and that Python 3.14 adds t-strings, which produce objects for custom processing rather than finished formatted strings.

### Source excerpt

Explore Python's modern string formatting tools, and learn to harness f-strings and the .format() method for interpolation and formatting.

## Python String Formatting: Available Tools and Their Features

DevFeed: [Python String Formatting: Available Tools and Their Features](<https://devfeed.tech/articles/python-string-formatting-available-tools-and-their-features-98860.md>)

Original publisher: [Read original article](<https://realpython.com/python-string-formatting/>)

Author: Leodanis Pozo Ramos

Published: 2026-10-24T14:00:00Z

Content type: tutorial

Language: en

Sources: [Real Python](<https://devfeed.tech/sources/real-python.md>)

Topics: [formatting](<https://devfeed.tech/topics/formatting.md>), [Python](<https://devfeed.tech/topics/python.md>)

Tags: [align](<https://devfeed.tech/tags/align.md>), [alignment](<https://devfeed.tech/tags/alignment.md>), [conversion](<https://devfeed.tech/tags/conversion.md>), [data-type](<https://devfeed.tech/tags/data-type.md>), [data-types](<https://devfeed.tech/tags/data-types.md>), [f](<https://devfeed.tech/tags/f.md>), [features](<https://devfeed.tech/tags/features.md>), [format](<https://devfeed.tech/tags/format.md>), [formatting](<https://devfeed.tech/tags/formatting.md>), [operator](<https://devfeed.tech/tags/operator.md>), [python](<https://devfeed.tech/tags/python.md>), [string](<https://devfeed.tech/tags/string.md>), [strings](<https://devfeed.tech/tags/strings.md>), [tool](<https://devfeed.tech/tags/tool.md>), [tools](<https://devfeed.tech/tags/tools.md>)

### AI overview

Python offers f-strings, `str.format()`, and the older `%` operator for interpolating and formatting values. F-strings suit readable eager interpolation; `.format()` supports reusable templates filled later and also uses Python's formatting mini-language. That mini-language provides alignment, numeric formatting, type conversion, and dynamic formatting, illustrated with report templates. The `%` operator supports positional or named fields, width, precision, and flags, but lacks the mini-language's broader options and is mainly encountered in legacy code. The tutorial compares these tradeoffs and demonstrates formatting student and sales reports.

### Source excerpt

Learn how Python string formatting works with f-strings, the .format() method, and the modulo operator, plus the strengths of each tool.

## Post-quantum website certificates from Cloudflare are scheduled for early 2027

DevFeed: [Post-quantum website certificates from Cloudflare are scheduled for early 2027](<https://devfeed.tech/articles/post-quantum-website-certificates-from-cloudflare-are-scheduled-for-early-2027-62202.md>)

Original publisher: [Read original article](<https://www.helpnetsecurity.com/2026/09/30/cloudflare-certificate-authority-2027/>)

Author: Mirko Zorz

Published: 2026-09-30T03:09:51Z

Content type: news

Language: en

Sources: [Help Net Security](<https://devfeed.tech/sources/help-net-security.md>)

Topics: [Certificate Transparency](<https://devfeed.tech/topics/certificate-transparency.md>), [Post-quantum cryptography](<https://devfeed.tech/topics/post-quantum-cryptography.md>), [Cryptography](<https://devfeed.tech/topics/cryptography.md>), [certificates](<https://devfeed.tech/topics/certificates.md>), [Cloudflare](<https://devfeed.tech/topics/cloudflare.md>), [enterprise certificate authority certificates](<https://devfeed.tech/topics/enterprise-certificate-authority-certificates.md>), [let's encrypt](<https://devfeed.tech/topics/let-s-encrypt.md>)

Tags: [certificate-authority](<https://devfeed.tech/tags/certificate-authority.md>), [certificates](<https://devfeed.tech/tags/certificates.md>), [cloudflare](<https://devfeed.tech/tags/cloudflare.md>), [encryption](<https://devfeed.tech/tags/encryption.md>), [f](<https://devfeed.tech/tags/f.md>), [merkle-tree](<https://devfeed.tech/tags/merkle-tree.md>), [merkle-tree-certificates](<https://devfeed.tech/tags/merkle-tree-certificates.md>), [news](<https://devfeed.tech/tags/news.md>), [post-quantum](<https://devfeed.tech/tags/post-quantum.md>), [quantum-computing](<https://devfeed.tech/tags/quantum-computing.md>), [security](<https://devfeed.tech/tags/security.md>)

### AI overview

Cloudflare plans to become a public certificate authority, issuing conventional certificates and post-quantum Merkle Tree Certificates. Production issuance of the post-quantum certificates is scheduled for the first quarter of 2027, while its applications to browser root programs remain pending. The company says the certificates use lightweight proofs to let browsers check trusted registry entries without sending heavy post-quantum signatures with every connection.

### Source excerpt

Cloudflare plans to become a public certificate authority (CA), an organization that issues the digital certificates websites use to encrypt traffic and prove who they are. The company said that its CA will issue conventional certificates and a post-quantum type called Merkle Tree Certificates (MTCs), with production MTC issuance scheduled for the first quarter of 2027. Cloudflare says much of the web's certificate issuing rests on a small set of dominant CAs, so one failure ... More -> The post Post-quantum website certificates from Cloudflare are scheduled for early 2027 appeared first on Help Net Security.

## The Liskov Substitution Principle does more than you think

DevFeed: [The Liskov Substitution Principle does more than you think](<https://devfeed.tech/articles/the-liskov-substitution-principle-does-more-than-you-think-25507.md>)

Original publisher: [Read original article](<https://buttondown.com/hillelwayne/archive/the-liskov-substitution-principle-does-more-than/>)

Author: Hillel Wayne

Published: 2026-01-06T16:51:26Z

Content type: article

Language: en

Sources: [Newsletter feed for Hillel Wayne's Newsletter](<https://devfeed.tech/sources/newsletter-feed-for-hillel-wayne-s-newsletter.md>)

Topics: [Object-oriented programming (OOP)](<https://devfeed.tech/topics/oop.md>), [superclass](<https://devfeed.tech/topics/superclass.md>)

Tags: [call](<https://devfeed.tech/tags/call.md>), [code](<https://devfeed.tech/tags/code.md>), [example](<https://devfeed.tech/tags/example.md>), [execution](<https://devfeed.tech/tags/execution.md>), [f](<https://devfeed.tech/tags/f.md>), [history](<https://devfeed.tech/tags/history.md>), [inheritance](<https://devfeed.tech/tags/inheritance.md>), [invariants](<https://devfeed.tech/tags/invariants.md>), [logic-for-programmers](<https://devfeed.tech/tags/logic-for-programmers.md>), [lsp](<https://devfeed.tech/tags/lsp.md>), [oop](<https://devfeed.tech/tags/oop.md>), [operator](<https://devfeed.tech/tags/operator.md>), [paper](<https://devfeed.tech/tags/paper.md>), [root](<https://devfeed.tech/tags/root.md>), [solid](<https://devfeed.tech/tags/solid.md>), [solid-principles](<https://devfeed.tech/tags/solid-principles.md>), [square](<https://devfeed.tech/tags/square.md>), [subtype](<https://devfeed.tech/tags/subtype.md>), [tests](<https://devfeed.tech/tags/tests.md>), [wing](<https://devfeed.tech/tags/wing.md>)

### AI overview

The excerpt presents Liskov substitution as a behavioral guarantee beyond merely using inheritance: any property that holds for a supertype should also hold for its subtype. It gives three conditions for correct subtyping: subtype methods must have equal or weaker preconditions and equal or stronger postconditions; the subtype must preserve the supertype's state invariants; and it must preserve its history properties, such as keeping an immutable field immutable. The author focuses on method contracts and says the first condition can be formally deduced, but the excerpt ends before showing that derivation.

### Source excerpt

Happy New Year! I'm done with the newsletter hiatus and am going to try updating weekly again. To ease into things a bit, I'll try to keep posts a little more off the cuff and casual for a while, at least until Logic for Programmers is done. Speaking of which, v0.13 should be out by the end of this month. So for this newsletter I want to talk about the Liskov Substitution Principle (LSP). Last week I read A SOLID Load of Bull by cryptographer Loupe Vaillant, where he argues the SOLID principles of OOP are not worth following. He makes an exception for LSP, but also claims that it's "just subtyping" and further: If I were trying really hard to be negative about the Liskov substitution principle, I would stress that it only applies when inheritance is involved, and inheritance is strongly discouraged anyway. LSP is more interesting than that! In the original paper, A Behavioral Notion of Subtyping, Barbara Liskov and Jeannette Wing start by defining a "correct" subtyping as follows: Subtype Requirement: Let ϕ(x) be a property provable about objects x of type T. Then ϕ(y) should be true for objects y of type S where S is a subtype of T. From then on, the paper determine what guarantees that a subtype is correct.1 They identify three conditions: Each of the subtype's methods has the same or weaker preconditions and the same or stronger postconditions as the corresponding supertype method.2 The subtype satisfies all state invariants of the supertype. The subtype satisfies all "history properties" of the supertype. 3 e.g. if a supertype has an immutable field, the subtype cannot make it mutable. (Later, Elisa Baniassad and Alexander Summers would realize these are equivalent to "the subtype passes all black-box tests designed for the supertype", which I wrote a little bit more about here.) I want to focus on the first rule about preconditions and postconditions. This refers to the method's contract. For a function f, f.Pre is what must be true going into the function, and