Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1511.08447

Decidability and Complexity for Quiescent Consistency and its Variations

Brijesh Dongol·Robert M. Hierons
View original source ↗Read source document ↗Export metadata ↓

Abstract

Quiescent consistency is a notion of correctness for a concurrent object that gives meaning to the object's behaviours in quiescent states, i.e., states in which none of the object's operations are being executed. Correctness of an implementation object is defined in terms of a corresponding abstract specification. This gives rise to two important verification questions: membership (checking whether a behaviour of the implementation is allowed by the specification) and correctness (checking whether all behaviours of the implementation are allowed by the specification). In this paper, we show that the membership problem for quiescent consistency is NP-complete and that the correctness problem is decidable, but coNP-hard and in EXPSPACE. For both problems, we consider restricted versions of quiescent consistency by assuming an upper limit on the number of events between two quiescent points. Here, we show that the membership problem is in PTIME, whereas correctness is in PSPACE. Quiescent consistency does not guarantee sequential consistency, i.e., it allows operation calls by the same process to be reordered when mapping to an abstract specification. Therefore, we also consider quiescent sequential consistency, which strengthens quiescent consistency with an additional sequential consistency condition. We show that the unrestricted versions of membership and correctness are NP-complete and undecidable, respectively. When by placing a limit on the number of events between two quiescent points, membership is in PTIME, while correctness is in PSPACE. Finally, we consider a version of quiescent sequential consistency that places an upper limit on the number of processes for every run of the implementation, and show that the membership problem for quiescent sequential consistency with this restriction is in PTIME.

Explore related subjects

cs.LOcs.DCcs.DScs.FL

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Brijesh Dongol, Robert M. Hierons. 2015-11-26. Decidability and Complexity for Quiescent Consistency and its Variations. https://arxiv.org/abs/1511.08447

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

KEEP EXPLORING

Related papers

arXiv2026

Differential Equations as Fixpoints and Games

Games and fixpoints are unified by proving that first-order game logic GL and the first-order modal mu-calculus L_mu are proved to be equiexpressive and equivalent, thereby fully aligning their expressive and deductive power. That is, there is a semantics-preserving translation from GL to L_mu, and vice versa. And both translations are provability-preserving, while equivalence with there-and-back-again roundtrip translations are provable in both calculi. This is to be contrasted with the propositional case, where game logic is strictly less expressive than the modal mu-calculus (without adding sabotage games). The extensions with differential equations, differential game logic (dGL) and differential modal mu-calculus, are also proved equiexpressive and equivalent. Moreover, as the continuous dynamics are definable by fixpoints or via games, ODEs can be axiomatized completely and, as a consequence, infinitesimally robust properties of ODEs can be decided via proof search. Rational gameplay provably collapses the games into single-player games to yield a strong arithmetical completeness theorem for dGL with rational-time ODEs.

cs.LO↗
arXiv2026

Self-extensional logics of formal inconsistency: Decidability and limits for paraconsistency

RmbC is a self-extensional paraconsistent logic in the family of Logics of Formal Inconsistency (LFIs). This system is obtained from mbC (the basic LFI) by adding the replacement property via two global inference rules. RmbC is characterized by a non-explosive negation $\neg$ and a consistency operator $\circ$, which recovers the principle of explosion in a controlled way. Together with its principal axiomatic extensions, RmbC admits a standard Lindenbaum-Tarski algebraization, with Boolean algebras with LFI operators (BALFIs) as its algebraic semantics. In this paper, we study how far this self-extensional paraconsistent behavior can be extended axiomatically, starting from RmbC. We classify pairs of very natural consistency axioms according to whether they preserve paraconsistency or force classical collapse; identify six minimal explosive combinations that collapse to a single algebraic core; and isolate a separate structural obstruction for the combination of excluded middle for $\neg$ with an involutive negation. We also investigate, for the first time, the decidability of this family of self-extensional LFIs. As a first result, we prove the finite model property for RmbC with respect to BALFI semantics via an algebraic filtration, which yields decidability, and transfer this result to several paraconsistent axiomatic extensions of RmbC. Finally, we establish a coNEXPTIME upper bound for the validity problem of RmbC and a coNP-hardness lower bound, and prove coNP-completeness for the principal extensions containing one of the six minimal explosive pairs.

cs.LO↗
arXiv2026

The Stochastic Target Discounted-Sum Problem

The target discounted-sum problem (TDS) asks, given a finite integer alphabet $Σ$, a rational discount factor $λ$, and a rational target $t$, whether some infinite sequence over $Σ$ has discounted sum exactly $t$. This problem remains open and underlies several open questions in automata theory, games, and Markov decision processes. We introduce and solve its stochastic counterpart, the stochastic target discounted-sum problem, which replaces existence by computation of the probability. We show that the probability that a random sequence generated by a finite Markov chain has discounted sum $t$ is rational and computable in pseudo-polynomial time. We further show how to decide, in polynomial time, whether the discounted-sum distribution of a Markov chain is atomless, and how to approximate to an arbitrary precision the probability that the discounted sum exceeds a rational threshold. Our techniques for the stochastic TDS problem allow us to make progress on TDS objectives in stochastic games, which are known to be as hard as the TDS problem. Restricting the maximizing player to finite-memory strategies, while allowing the minimizing player to use arbitrary strategies, we reduce the value problem and the synthesis problem to corresponding problems for safety objectives in stochastic games. This yields computable optimal values and deterministic optimal strategies with pseudo-polynomially bounded memory for stochastic games, and results in pseudo-polynomial-time algorithms for special cases of Markov decision processes and deterministic two-player games.

cs.LO↗