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Linearizability is a correctness criterion for concurrent systems. In this report, we describe how temporal logic can be used to prove linearizability of a concurrent lock-free stack implementation. ... The logic used is an extended variant of Interval Temporal Logic, which is integrated in the KIV interactive theorem prover. ... This allows us to mix programs with temporal logic formulas. Program operators describe only system steps that alternate with arbitrary environment steps. ...doi:10.1007/s00165-009-0130-y fatcat:6sko4xbiu5afhbyqzib455fhva
It then sketches our approach to the modular verification of lock-free algorithms which uses relyguarantee reasoning and a powerful temporal logic to derive refinement proof obligations that can be verified ... with the interactive theorem prover KIV. ... Our own approach uses an expressive temporal logic  ,  that is a variant of interval temporal logic (ITL,  ). ...doi:10.1109/acsd.2009.10 dblp:conf/acsd/SchellhornB09 fatcat:2ou44pua5fhe7ovdrqpruere2u
A relation between what actually happens (temporal order) and what seems to happen (logical order) is argued to be necessary. An alternative definition is proposed. ... The definition of sequential consistency is compared with an intuitive notion of correctness. ... response in the temporal order is also the i th response in the logical order.For another example, we have the following result for linearizability: Lemma 2 For a linearizable system, b l = p − 1 where ...doi:10.1016/j.ipl.2005.09.002 fatcat:qx7bjavlebfpjkxr3zeaagj2qi
Proving linearizability of concurrent data structures remains a key challenge for verification. ... We substantiate the usefulness of our development by verifying the linearizability of the Logical Ordering (LO-)tree and RDCSS. ... The proof exercises the full power of our logic by combing a linearizability argument based on temporal interpolation with local reasoning in separation logic to handle the functional correctness specification ...arXiv:2209.13692v1 fatcat:mdu5h4vinzgwpmtm4npronz5ga
Lecture Notes in Computer Science
We highlight the power of this lemma when combined with our generalized version of the classical Hindsight Lemma, which enables us to prove linearizability by reasoning about the temporal properties of ... the operations instead of reasoning about the linearizability points directly. ... So we know that no leaf node with key k exists in state σ d . The linearizability of effectful operations, which have fixed linearizability points, are not hard to prove. Lemma 6. ...doi:10.1007/978-3-319-26850-7_11 fatcat:lm5ft7kjmvb5lb2fae7w5rwjue
Our main tools are metric and layered temporal logics originally proposed to model time granularity in various contexts. ... in computer science concentrated on the so-called (real-time) temporal logics of programs that take state as a primitive notion, and define time as an attribute of states. ... In order to deal with real-time systems, such logics have been provided with a metric of time, e.g.  . ...doi:10.1093/jigpal/8.5.681 fatcat:fvyi3jbdsvfitat4y7jhmz4r7y
Proving the linearizability of highly concurrent data structures, such as those using optimistic concurrency control, is a challenging task. ... We present a unifying proof argument for the correctness of unsynchronized traversals, and apply it to prove the linearizability of several highly concurrent search data structures, including an optimistic ... Proving Linearizability Proving linearizability of an algorithm like ours is challenging because searches are performed with no synchronization. ...doi:10.4230/lipics.disc.2018.23 dblp:conf/wdag/FeldmanE0RS18 fatcat:j7scjaexjvezflts5amsdjrhlq
We present a proof of safety and linearizability of a highlyconcurrent optimistic set algorithm. ... Proving Linearizability with Hindsight Theorem 7.5 proves the linearizability of the set algorithm shown in Fig. 1 with respect to the set's sequential specification shown in Fig. 2 . ... Wait freedom follows. 2 LINEARIZABILITY BY HINDSIGHT In this section, we describe the notion of linearizability and prove that the concurrent set algorithm shown in Fig. 1 is linearizable with respect ...doi:10.1145/1835698.1835722 dblp:conf/podc/OHearnRVYY10 fatcat:aetlxymgljfbjbzby4ly4eb2ie
In this paper we propose a new method, based on a separation-style logic, for reasoning about concurrent objects with such linearization points. ... For example, modifying a temporal position of a linearization point can be modeled similarly to a pointer update in separation logic. ... Proving linearizability using partial orders. Concurrently with us, Khyzha et al. ...doi:10.4230/lipics.ecoop.2017.8 dblp:conf/ecoop/DelbiancoSNB17 fatcat:wfdklnzngnavdgl4mzg2i5knam
In this paper we propose a new method, based on a separation-style logic, for reasoning about concurrent objects with such linearization points. ... For example, modifying a temporal position of a linearization point can be modeled similarly to a pointer update in separation logic. ... Proving linearizability using partial orders. Concurrently with us, Khyzha et al. ...arXiv:1604.08080v4 fatcat:qx57mqa3vvh7fnng4hglb5wqeu
applications to temporal logic. ... In this paper, first, we introduce a new temporal logic called infinitary regular temporal logic (ooRTL), which is able to describe fairness, and show that its expressive power is equivalent to the class ...
I will discuss work on layering analysis for consensus, generalizations to other problems using topology  , and iterated models together with recursive distributed algorithms [3, 4]. ... In the first part, we study the expressive power of first-order logic, establish connections with temporal logics and propositional dynamic logic, and present a normal-form construction. ... First-order logic captures many interesting properties of distributed systems, and it subsumes various temporal logics. ...doi:10.4230/dagrep.8.5.60 dblp:journals/dagstuhl-reports/EsparzaFMR18 fatcat:72a6n5b32bd7rh7bgl4fb64fmy
Ehrenfeucht-Fraissé games, a tech- nique for proving results on expressiveness of logical languages involving quantification, are briefly described. ... Three notions of correctness (serializability, linearizability, and sequen- tial consistency) are considered. ...
Linearizability is a key correctness criterion for concurrent data structures, ensuring that each history of the concurrent object under consideration is consistent with respect to a history of the corresponding ... The sophisticated nature of concurrent objects means that linearizability is difficult to judge, and hence, over the years, numerous techniques for verifying linearizability have been developed using a ... For example, have developed a framework that combines interval temporal logic, rely/guarantee and simulation proofs. ...doi:10.1145/2796550 fatcat:q7a5zsxqrzawbd5mhl4lxmy2vi
ATVA 2015 had 95 regular and 13 tool submissions, with 33 papers accepted (six of them are tool papers). ... logic formulas. ... They have proven that some of the window mean-payoff objectives are decidable in games with partial observation. • TSO to TSO linearizability is undecidable by Chao Wang, Yi Lv, Peng Wu. ...doi:10.1007/s00236-018-0330-0 fatcat:g7gcqdqihzfixbycj2xaybc63q
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