arXiv subjects

Bryan Ford

Publications and source records attributed to Bryan Ford.

At least 19 recordsLinked to original sources

arXiv2026

Coinduction in Grounded Arithmetic

A grounded arithmetic counts a sentence as true only when a terminating process establishes it; a sentence no such process settles has no value. Such a logic can state that an event happens, but not that it never happens under unbounded choice. This paper extends such a logic so that it can. The base is Reflective Grounded Arithmetic (RGA) with Inductive Grounded Arithmetic (IGA)'s least-fixed-point reading and ground induction. It adds a separate greatest-fixed-point former $ν$ with Park's coinduction rule, proves that one former cannot carry both ground induction and coinduction, and adds a dichotomy rule: the classical disjunction between a least-fixed-point atom and the greatest-fixed-point atom of its dual, under a derivable premise that the body's leaves are decided. The systems are sound for an explicit model reading every $ν$-body at its greatest fixed point, hence consistent; they agree with the least model wherever it has a value and prove sentences it leaves without one. The dichotomy replaces the underivable hypothesis that an order is well-founded by the derivable one that its steps are decided; the change of model pays for the move. With ground induction the dichotomy derives the omniscience rule of the sibling arithmetic OGA, so the system has no semantics whose certificates for universals are its own proofs. The systems prove, as single sentences, that every decided tree is well-founded or has an infinite branch given by a term, total in the new model; that random assignment terminates while its divergent twin runs forever; that a fair loop terminates and the alternating-bit protocol delivers every message; that open games are determined; that the termination gap in Nakata and Uustalu's trace semantics closes; and that Cinderella wins the bucket game at capacity three. Isabelle/HOL checks every result.

math.LO↗

arXiv2026

Internal Reasoning and Consistency in Reflective Grounded Arithmetic

Reflective Grounded Arithmetic (RGA) is a paracomplete arithmetic allowing direct expression of any general-recursive computation. Every RGA term is a program and truth is grounded evaluation, with a proof certificate at each universal quantifier. This paper shows, in a machine-checked Isabelle/HOL development, that such a system is powerful enough to carry out its own metamathematics. A fuel-indexed decider of RGA's grounded semantics and checkers for RGA's proofs are compiled primitive-recursive RGA terms. RGA proves internally that its decider never affirms $0 = 1$, and that every well-formed term it affirms has an RGA proof accepted by a transparent test. RGA proves that, for each valid RGA proof, its conclusion is true. RGA proves that each grounded-true well-formed term is provable. RGA proves that no proof in either of two decided classes of RGA proofs derives $0 = 1$. Gödel's incompleteness theorems hold for RGA, but their proofs must be adapted. In RGA an implication $A \rightarrow B$ is strictly stronger than an entailment $A \vdash B$: RGA discharges a hypothesis only when it can prove the hypothesis decided, a restriction needed to defuse Curry's paradox. RGA's implication is material and RGA has the disjunction property, so RGA proves no implication between ungrounded sentences. The implications that the textbook proof of Gödel's second theorem uses are of this kind and fail, but the entailments and rules it uses hold: Gödel's proof survives as entailments. RGA does not prove its consistency sentence $\mathit{Con}$: RGA carries out Gödel's argument internally, with a decided proof predicate and explicit proof transformers, and only the last step, that RGA does not prove $0 = 1$, is left to HOL. RGA also proves its own second incompleteness theorem as an entailment from $\mathit{Con}$, and as a single sentence quantified over proofs.

math.LO↗

arXiv2026

Inductive Grounded Arithmetic: Goodstein, the Hydra, and $Γ_0$

What does a recursive definition mean when the logic is grounded, so a sentence is true only if a terminating process makes it so? Kripke's answer for the special case of truth was the least fixed point. This paper takes that answer as a rule. Reflective Grounded Arithmetic (RGA) already writes any recursive definition as one self-referential term, paradoxes included. Inductive Grounded Arithmetic (IGA) adds the elimination rule for every positive one, so that accessibility, the winning positions of a game, and grounded truth itself each come with their own induction principle. The rule is sound for the omega model and the system is consistent, both machine-checked in Isabelle/HOL. With the rule, IGA proves Goodstein's theorem outright, in a logic without implication at an undecided hypothesis, and the Kirby-Paris hydra game for primitive recursive strategies, both with every step of the arithmetic a grounded derivation. It proves the Cantor normal forms well-founded, from which the well-foundedness of the standard $\varepsilon_0$ notation system in HOL follows, and it certifies the Veblen notation as an ordinal below every $φ(n,0)$. It defines Kripke truth for RGA's own language as one fixed point that agrees with the omega model exactly. Two equivalences locate what the classical world has and the grounded one does not. IGA proves the whole Veblen notation well-founded exactly when it admits bivalence of accessibility for that order, and bivalence of accessibility for an order is sound exactly when the order is well-founded; so $Γ_0$ lies at most one instance of excluded middle away, at the accessibility predicate of the notation, and that instance, the well-foundedness sentence and one membership claim in a primitive-recursive form of Kleene's $\mathcal O$ are interderivable over IGA.

math.LO↗

arXiv2026

Computable Quantification in Reflective Grounded Arithmetic

Informal statements of Gödel's incompleteness theorems often run: "any consistent formal system with arithmetic has true but unprovable statements." That reading assumes a classical notion of truth, under which a universal statement is true as soon as each of its numeral instances is. This paper presents reflective grounded arithmetic (RGA), in which truth is grounded in computation and universal quantification is grounded reflectively: a universal statement is true when the system's own proof search certifies its schematic instance, and false when the system refutes one numeral instance. RGA allows recursive definitions without restriction and proves addition, multiplication and Ackermann's function total as theorems quantified inside the system. RGA is consistent, and it is complete for its own, grounded notion of truth: every well-formed statement that evaluates to true is provable. Gödel's theorems still hold for RGA, as a companion paper shows. The statements that classical reasoning calls true but unprovable have every numeral instance provable but no certified schematic instance, so they are ungrounded in RGA; read instance by instance, in an $ω$-semantics for which RGA is also sound, they are true. All results are machine-checked in Isabelle/HOL: soundness and consistency; completeness for grounded truth, open statements included; $ω$-soundness and $ω$-consistency; that grounded truth is recursively enumerable and RGA represents exactly the recursively enumerable sets; and $ω$-incompleteness. The logic is neither classical nor intuitionistic: double negation is eliminable as an entailment, excluded middle fails wherever a statement has no boolean value, RGA has the disjunction and witness properties, and the deduction theorem holds exactly at provably decided hypotheses.

math.LO↗

arXiv2026

Towards the ideals of Self-Recovery and Metadata Privacy in Social Vault Recovery with Apollo

Social recovery enables users to enlist trusted contacts, or trustees, to help recover lost access to end-to-end-encrypted repositories or vaults. However, existing recovery mechanisms often make strong memorability assumptions about what users will remember. Weakening these memorability assumptions to increase the robustness of recovery is possible, but may leak sensitive metadata about the user and/or trustees if done naively. This paper's first contribution is to draw attention to and formalize this basic tension between memorability and metadata privacy in social vault recovery. Our second contribution is Apollo, a social recovery mechanism that aims to avoid any memorability assumptions while strongly protecting recovery metadata privacy. Apollo approximates the ideal of self-recovery by relying only on a threshold of social reconnection events, which may be initiated either by the user or the user's contacts. Apollo thereby has a chance of succeeding in vault recovery even in a worst-case scenario where the user has forgotten all metadata, including even the vault's existence. To protect the metadata's privacy, Apollo distributes either real or fake (chaff) data to all of a user's contacts, not just the user's trustees, thus systematically anonymizing the trustees among the larger set of contacts. To make this anonymity set scalable, Apollo uses a novel multi-layered secret sharing scheme to mitigate the computational overhead of recovery in this setting, which would otherwise be exponential in the recovery threshold. Finally, we evaluate a prototype implementation of Apollo. Apollo reduces the probability of malicious recovery to under 0.1% for an adversary capable of obtaining shares from every 1-out-of-2 contacts. After reconnecting with 30 contacts, the multi-layered design shows an improvement of 5 orders in computation time, compared to a single-layered approach.

cs.CR↗

arXiv2026

Idealizing Useful Fictions in Omega Grounded Arithmetic

Grounded arithmetic is a family of formal systems for reasoning about computation in which a statement may be asserted only when a terminating computation backs it; the logics are paracomplete - for a sentence whose backing computation never settles, neither the sentence nor its negation is derivable, so paradoxes like the Liar are harmless rather than explosive. The reflective member of the family, RGA, can quantify over its own computations, but cannot certify that its own unbounded searches have definite yes-or-no answers. This paper studies what happens when that openness is closed by exactly one rule - ATI, the $ω$-grounded universal: if every numeric instance of a universal sentence is certified decided, the universal is certified decided. The resulting system, OGA, shares RGA's syntax and rules symbol-for-symbol otherwise, and every consequence is developed as a machine-checked theorem. Decidedness certificates become abundant - every totality question about a computable function is certified to have an answer, whether or not anyone can produce it - and this is exactly the provable separation between the two systems. OGA is complete for its own semantics; certified-but-unresolved sentences receive values built from the system's own open questions. Provability remains recursively enumerable, with a primitive-recursive certificate checker, while $ω$-truth deliberately is not. Within that asymmetry, incompleteness takes a new form. The Gödel sentence is classified, unconditionally, as a genuine fiction: neither provable nor refutable, yet valued, and carrying a computable pedigree recording exactly what adopting it as an axiom commits one to. The adoption is itself a theorem suite: extending OGA by any finite stock of true fictions is consistent, and independently certified adoptions can never collide.

math.LO↗

arXiv2026

Have a thing? Reasoning around recursion with dynamic typing in grounded arithmetic

Neither the classical nor intuitionistic logic traditions are perfectly aligned with the purpose of reasoning about computation, as neither can permit unconstrained recursive definitions without inconsistency: recursive definitions must normally be proven terminating before admission and use. Grounded arithmetic or GA is a formal-reasoning foundation allowing direct expression of arbitrary recursive definitions. GA adjusts traditional inference rules so that terms that express nonterminating computations harmlessly denote no semantic value ($\bot$) instead of yielding inconsistency. Recursive functions are proven terminating in GA essentially by "dynamically typing" terms, or equivalently, symbolically reverse-executing the computations they denote via inference rules. Once recursive functions have been proven terminating, logical reasoning about them reduces to familiar classical rules. We summarize the development and lessons learned from two mechanically-checked formulations of GA, finding both syntactically consistent and semantically sound with respect to an underlying computable model. Propositional grounded arithmetic or PGA is a quantifier-free system for inductive grounded reasoning about open formulas. PGA has logical expressiveness comparable to Skolem's PRA, but has general-recursive (Turing-complete) functional expressiveness. PGA builds upon a simpler system of basic grounded arithmetic or BGA, which omits logical operators entirely. BGA and PGA are not only sound but semantically complete, a combination impossible for powerful classical systems with arithmetic, due to Gödel's incompleteness theorems. These results suggest that powerful and consistent formal reasoning with unconstrained recursive definitions is possible, potentially enabling new computation-centric formal languages, proof assistants, and type systems in the future.

cs.PL↗

arXiv2025

TRIP: Coercion-resistant Registration for E-Voting with Verifiability and Usability in Votegral

Online voting is convenient and flexible, but amplifies the risks of voter coercion and vote buying. One promising mitigation strategy enables voters to give a coercer fake voting credentials, which silently cast votes that do not count. Current systems along these lines make problematic assumptions about credential issuance, however, such as strong trust in a registrar and/or in voter-controlled hardware, or expecting voters to interact with multiple registrars. Votegral is the first coercion-resistant voting architecture that leverages the physical security of in-person registration to address these credential-issuance challenges, amortizing the convenience costs of in-person registration by reusing credentials across successive elections. Votegral's registration component, TRIP, gives voters a kiosk in a privacy booth with which to print real and fake credentials on paper, eliminating dependence on trusted hardware in credential issuance. The voter learns and can verify in the privacy booth which credential is real, but real and fake credentials thereafter appear indistinguishable to others. Only voters actually under coercion, a hopefully-rare case, need to trust the kiosk. To achieve verifiability, each paper credential encodes an interactive zero-knowledge proof, which is sound in real credentials but unsound in fake credentials. Voters observe the difference in the order of printing steps, but need not understand the technical details. Experimental results with our prototype suggest that Votegral is practical and sufficiently scalable for real-world elections. User-visible latency of credential issuance in TRIP is at most 19.7 seconds even on resource-constrained kiosk hardware. A companion usability study indicates that TRIP's usability is competitive with other e-voting systems, and formal proofs support TRIP's combination of coercion-resistance and verifiability.

cs.CR↗

arXiv2025

Reasoning Around Paradox with Grounded Deduction

How can we reason around logical paradoxes without falling into them? This paper introduces grounded deduction or GD, a Kripke-inspired approach to first-order logic and arithmetic that is neither classical nor intuitionistic, but nevertheless appears both pragmatically usable and intuitively justifiable. GD permits the direct expression of unrestricted recursive definitions -- including paradoxical ones such as 'L := not L' -- while adding dynamic typing premises to certain inference rules so that such paradoxes do not lead to inconsistency. This paper constitutes a preliminary development and investigation of grounded deduction, to be extended with further elaboration and deeper analysis of its intriguing properties.

math.LO↗

arXiv2024

Baxos: Backing off for Robust and Efficient Consensus

Leader-based consensus algorithms are vulnerable to liveness and performance downgrade attacks. We explore the possibility of replacing leader election in Multi-Paxos with random exponential backoff (REB), a simpler approach that requires minimum modifications to the two phase Synod Paxos and achieves better resiliency under attacks. We propose Baxos, a new resilient consensus protocol that leverages a random exponential backoff scheme as a replacement for leader election in consensus algorithms. Our backoff scheme addresses the common challenges of random exponential backoff such as scalability and robustness to changing wide area latency. We extensively evaluate Baxos to illustrate its performance and robustness against two liveness and performance downgrade attacks using an implementation running on Amazon EC2 in a wide area network and a combination of a micro benchmark and YCSB-A workload on Redis. Our results show that Baxos offers more robustness to liveness and performance downgrade attacks than leader-based consensus protocols. Baxos outperforms Multi-Paxos and Raft up to 128% in throughput under liveness and performance downgrade attacks under worst case contention scenarios where each replica proposes requests concurrently.

cs.DC↗

arXiv2024

E-Vote Your Conscience: Perceptions of Coercion and Vote Buying, and the Usability of Fake Credentials in Online Voting

Online voting is attractive for convenience and accessibility, but is more susceptible to voter coercion and vote buying than in-person voting. One mitigation is to give voters fake voting credentials that they can yield to a coercer. Fake credentials appear identical to real ones, but cast votes that are silently omitted from the final tally. An important unanswered question is how ordinary voters perceive such a mitigation: whether they could understand and use fake credentials, and whether the coercion risks justify the costs of mitigation. We present the first systematic study of these questions, involving 150 diverse individuals in Boston, Massachusetts. All participants "registered" and "voted" in a mock election: 120 were exposed to coercion resistance via fake credentials, the rest forming a control group. Of the 120 participants exposed to fake credentials, 96% understood their use. 53% reported that they would create fake credentials in a real-world voting scenario, given the opportunity. 10% mistakenly voted with a fake credential, however. 22% reported either personal experience with or direct knowledge of coercion or vote-buying incidents. These latter participants rated the coercion-resistant system essentially as trustworthy as in-person voting via hand-marked paper ballots. Of the 150 total participants to use the system, 87% successfully created their credentials without assistance; 83% both successfully created and properly used their credentials. Participants give a System Usability Scale score of 70.4, which is slightly above the industry's average score of 68. Our findings appear to support the importance of the coercion problem in general, and the promise of fake credentials as a possible mitigation, but user error rates remain an important usability challenge for future work.

cs.HC↗

arXiv2023

F3B: A Low-Overhead Blockchain Architecture with Per-Transaction Front-Running Protection

Front-running attacks, which benefit from advanced knowledge of pending transactions, have proliferated in the blockchain space since the emergence of decentralized finance. Front-running causes devastating losses to honest participants and continues to endanger the fairness of the ecosystem. We present Flash Freezing Flash Boys (F3B), a blockchain architecture that addresses front-running attacks by using threshold cryptography. In F3B, a user generates a symmetric key to encrypt their transaction, and once the underlying consensus layer has finalized the transaction, a decentralized secret-management committee reveals this key. F3B mitigates front-running attacks because, before the consensus group finalizes it, an adversary can no longer read the content of a transaction, thus preventing the adversary from benefiting from advanced knowledge of pending transactions. Unlike other mitigation systems, F3B properly ensures that all unfinalized transactions, even with significant delays, remain private by adopting per-transaction protection. Furthermore, F3B addresses front-running at the execution layer; thus, our solution is agnostic to the underlying consensus algorithm and compatible with existing smart contracts. We evaluated F3B on Ethereum with a modified execution layer and found only a negligible (0.026%) increase in transaction latency, specifically due to running threshold decryption with a 128-member secret-management committee after a transaction is finalized; this indicates that F3B is both practical and low-cost.

cs.CR↗

arXiv2023

Breaking Blockchain Rationality with Out-of-Band Collusion

Blockchain systems often rely on rationality assumptions for their security, expecting that nodes are motivated to maximize their profits. These systems thus design their protocols to incentivize nodes to execute the honest protocol but fail to consider out-of-band collusion. Existing works analyzing rationality assumptions are limited in their scope, either by focusing on a specific protocol or relying on non-existing financial instruments. We propose a general rational attack on rationality by leveraging an external channel that incentivizes nodes to collude against the honest protocol. Our approach involves an attacker creating an out-of-band bribery smart contract to motivate nodes to double-spend their transactions in exchange for shares in the attacker's profits. We provide a game theory model to prove that any rational node is incentivized to follow the malicious protocol. We discuss our approach to attacking the Bitcoin and Ethereum blockchains, demonstrating that irrational behavior can be rational in real-world blockchain systems when analyzing rationality in a larger ecosystem. We conclude that rational assumptions only appear to make the system more secure and offer a false sense of security under the flawed analysis.

cs.GT↗

arXiv2022

Matchertext: Towards Verbatim Interlanguage Embedding

Embedding text in one language within text of another is commonplace for numerous purposes, but usually requires tedious and error-prone "escaping" transformations on the embedded string. We propose a simple cross-language syntactic discipline, matchertext, which enables the safe embedding a string in any compliant language into a string in any other language via simple "copy-and-paste" - in particular with no escaping, obfuscation, or expansion of embedded strings. We apply this syntactic discipline to several common and frequently-embedded language syntaxes such as URIs, HTML, and JavaScript, exploring the benefits, costs, and compatibility issues in adopting the proposed matchertext discipline. One early matchertext-based language is MinML, a concise but general alternative syntax for writing HTML or XML.

cs.PL↗

arXiv2022

Limiting Lamport Exposure to Distant Failures in Globally-Managed Distributed Systems

Globalized computing infrastructures offer the convenience and elasticity of globally managed objects and services, but lack the resilience to distant failures that localized infrastructures such as private clouds provide. Providing both global management and resilience to distant failures, however, poses a fundamental problem for configuration services: How to discover a possibly migratory, strongly-consistent service/object in a globalized infrastructure without dependencies on globalized state? Limix is the first metadata configuration service that addresses this problem. With Limix, global strongly-consistent data-plane services and objects are insulated from remote gray failures by ensuring that the definitive, strongly-consistent metadata for any object is always confined to the same region as the object itself. Limix guarantees availability bounds: any user can continue accessing any strongly consistent object that matters to the user located at distance $Δ$ away, insulated from failures outside a small multiple of $Δ$. We built a Limix metadata service based on CockroachDB. Our experiments on Internet-like networks and on AWS, using realistic trace-driven workloads, show that Limix enables global management and significantly improves availability over the state-of-the-art.

cs.DC↗

arXiv2021

PriFi: Low-Latency Anonymity for Organizational Networks

Organizational networks are vulnerable to traffic-analysis attacks that enable adversaries to infer sensitive information from the network traffic - even if encryption is used. Typical anonymous communication networks are tailored to the Internet and are poorly suited for organizational networks. We present PriFi, an anonymous communication protocol for LANs, which protects users against eavesdroppers and provides high-performance traffic-analysis resistance. PriFi builds on Dining Cryptographers networks but reduces the high communication latency of prior work via a new client/relay/server architecture, in which a client's packets remain on their usual network path without additional hops, and in which a set of remote servers assist the anonymization process without adding latency. PriFi also solves the challenge of equivocation attacks, which are not addressed by related works, by encrypting the traffic based on the communication history. Our evaluation shows that PriFi introduces a small latency overhead (~100ms for 100 clients) and is compatible with delay-sensitive applications such as VoIP.

cs.CR↗

arXiv2020

Identity and Personhood in Digital Democracy: Evaluating Inclusion, Equality, Security, and Privacy in Pseudonym Parties and Other Proofs of Personhood

Digital identity seems like a prerequisite for digital democracy: how can we ensure "one person, one vote" online without identifying voters? But digital identity solutions - ID checking, biometrics, self-sovereign identity, and trust networks - all present flaws, leaving users vulnerable to exclusion, identity loss or theft, and coercion. These flaws may be insurmountable because digital identity is a cart pulling the horse. We cannot achieve digital identity secure enough for the weight of digital democracy, until we build it on a solid foundation of "digital personhood." While identity is about distinguishing one person from another through attributes or affiliations, personhood is about giving all real people inalienable digital participation rights independent of identity, including protection against erosion of their democratic rights through identity loss, theft, coercion, or fakery. We explore and analyze alternative approaches to "proof of personhood" that may provide this missing foundation. Pseudonym parties marry the transparency of periodic physical-world events with the power of digital tokens between events. These tokens represent limited-term but renewable claims usable for purposes such as online voting or liquid democracy, sampled juries or deliberative polls, abuse-resistant social communication, or minting universal basic income in a permissionless cryptocurrency. Enhancing pseudonym parties to provide participants a moment of enforced physical security and privacy can address coercion and vote-buying risks that plague today's E-voting systems. We also examine other proposed approaches to proof of personhood, some of which offer conveniences such as all-online participation. These alternatives currently fall short of satisfying all the key digital personhood goals, unfortunately, but offer valuable insights into the challenges we face.

cs.CY↗

arXiv2020

Economic Principles of PoPCoin, a Democratic Time-based Cryptocurrency

While democracy is founded on the principle of equal opportunity to manage our lives and pursue our fortunes, the forms of money we have inherited from millenia of evolution has brought us to an unsustainable dead-end of exploding inequality. PoPCoin proposes to leverage the unique historical opportunities that digital cryptocurrencies present for a "clean-slate" redesign of money, in particular around long-term equitability and sustainability, rather than solely stability, as our primary goals. We develop and analyze a monetary policy for PoPCoin that embodies these equitability goals in two basic rules that maybe summarized as supporting equal opportunity in "space" and "time": the first by regularly distributing new money equally to all participants much like a basic income, the second by holding the aggregate value of these distributions to a constant and non-diminishing portion of total money supply through demurrage. Through preliminary economic analysis, we find that these rules in combination yield a unique form of money with numerous intriguing and promising properties, such as a quantifiable and provable upper bound on monetary inequality, a natural "early adopter's reward" that could incentivize rapid growth while tapering off as participation saturates, resistance to the risk of deflationary spirals, and migration incentives opposite those created by conventional basic incomes.

cs.CY↗