{"title":"A Scalable Algorithm for Decentralized Actor Termination Detection","authors":"Dan Plyukhin, G. Agha","doi":"10.46298/lmcs-18(1:39)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(1:39)2022","url":null,"abstract":"Automatic garbage collection (GC) prevents certain kinds of bugs and reduces\u0000programming overhead. GC techniques for sequential programs are based on\u0000reachability analysis. However, testing reachability from a root set is\u0000inadequate for determining whether an actor is garbage: Observe that an\u0000unreachable actor may send a message to a reachable actor. Instead, it is\u0000sufficient to check termination (sometimes also called quiescence): an actor is\u0000terminated if it is not currently processing a message and cannot receive a\u0000message in the future. Moreover, many actor frameworks provide all actors with\u0000access to file I/O or external storage; without inspecting an actor's internal\u0000code, it is necessary to check that the actor has terminated to ensure that it\u0000may be garbage collected in these frameworks. Previous algorithms to detect\u0000actor garbage require coordination mechanisms such as causal message delivery\u0000or nonlocal monitoring of actors for mutation. Such coordination mechanisms\u0000adversely affect concurrency and are therefore expensive in distributed\u0000systems. We present a low-overhead deferred reference listing technique (called\u0000DRL) for termination detection in actor systems. DRL is based on asynchronous\u0000local snapshots and message-passing between actors. This enables a\u0000decentralized implementation and transient network partition tolerance. The\u0000paper provides a formal description of DRL, shows that all actors identified as\u0000garbage have indeed terminated (safety), and that all terminated actors--under\u0000certain reasonable assumptions--will eventually be identified (liveness).","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130396381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Determinisability of register and timed automata","authors":"Lorenzo Clemente, S. Lasota, Radoslaw Pi'orkowski","doi":"10.46298/lmcs-18(2:9)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(2:9)2022","url":null,"abstract":"The deterministic membership problem for timed automata asks whether the\u0000timed language given by a nondeterministic timed automaton can be recognised by\u0000a deterministic timed automaton. An analogous problem can be stated in the\u0000setting of register automata. We draw the complete decidability/complexity\u0000landscape of the deterministic membership problem, in the setting of both\u0000register and timed automata. For register automata, we prove that the\u0000deterministic membership problem is decidable when the input automaton is a\u0000nondeterministic one-register automaton (possibly with epsilon transitions) and\u0000the number of registers of the output deterministic register automaton is\u0000fixed. This is optimal: We show that in all the other cases the problem is\u0000undecidable, i.e., when either (1) the input nondeterministic automaton has two\u0000registers or more (even without epsilon transitions), or (2) it uses guessing,\u0000or (3) the number of registers of the output deterministic automaton is not\u0000fixed. The landscape for timed automata follows a similar pattern. We show that\u0000the problem is decidable when the input automaton is a one-clock\u0000nondeterministic timed automaton without epsilon transitions and the number of\u0000clocks of the output deterministic timed automaton is fixed. Again, this is\u0000optimal: We show that the problem in all the other cases is undecidable, i.e.,\u0000when either (1) the input nondeterministic timed automaton has two clocks or\u0000more, or (2) it uses epsilon transitions, or (3) the number of clocks of the\u0000output deterministic automaton is not fixed.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123909923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Point-free Construction of Real Exponentiation","authors":"Ming-fai Ng, S. Vickers","doi":"10.46298/lmcs-18(3:15)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(3:15)2022","url":null,"abstract":"We define a point-free construction of real exponentiation and logarithms,\u0000i.e. we construct the maps $expcolon (0, infty)times mathbb{R}\u0000rightarrow !(0,infty),, (x, zeta) mapsto x^zeta$ and $logcolon\u0000(1,infty)times (0, infty) rightarrowmathbb{R},, (b, y) mapsto\u0000log_b(y)$, and we develop familiar algebraic rules for them. The point-free\u0000approach is constructive, and defines the points of a space as models of a\u0000geometric theory, rather than as elements of a set - in particular, this allows\u0000geometric constructions to be applied to points living in toposes other than\u0000Set. Our geometric development includes new lifting and gluing techniques in\u0000point-free topology, which highlight how properties of $mathbb{Q}$ determine\u0000properties of real exponentiation.\u0000 This work is motivated by our broader research programme of developing a\u0000version of adelic geometry via topos theory. In particular, we wish to\u0000construct the classifying topos of places of $mathbb{Q}$, which will provide a\u0000geometric perspective into the subtle relationship between $mathbb{R}$ and\u0000$mathbb{Q}_p$, a question of longstanding number-theoretic interest.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"119 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116379692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Inductive and Coinductive Topological Generation with Church's thesis and the Axiom of Choice","authors":"M. Maietti, Samuele Maschio, M. Rathjen","doi":"10.46298/lmcs-18(4:5)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(4:5)2022","url":null,"abstract":"In this work we consider an extension MFcind of the Minimalist Foundation MF for predicative constructive mathematics with the addition of inductive and coinductive definitions sufficient to generate Sambin's Positive topologies, namely Martin-L\"of-Sambin formal topologies equipped with a Positivity relation (used to describe pointfree formal closed subsets). In particular the intensional level of MFcind, called mTTcind, is defined by extending with coinductive definitions another theory mTTind extending the intensional level mTT of MF with the sole addition of inductive definitions. In previous work we have shown that mTTind is consistent with Formal Church's Thesis CT and the Axiom of Choice AC via an interpretation in Aczel's CZF+REA. Our aim is to show the expectation that the addition of coinductive definitions to mTTind does not increase its consistency strength by reducing the consistency of mTTcind+CT+AC to the consistency of CZF+REA through various interpretations. We actually reach our goal in two ways. One way consists in first interpreting mTTcind+CT+AC in the theory extending CZF with the Union Regular Extension Axiom, REA_U, a strengthening of REA, and the Axiom of Relativized Dependent Choice, RDC. The theory CZF+REA_U+RDC is then interpreted in MLS*, a version of Martin-L\"of's type theory with Palmgren's superuniverse S. A last step consists in interpreting MLS* back into CZF+REA. The alternative way consists in first interpreting mTTcind+AC+CT directly in a version of Martin-L\"of's type theory with Palmgren's superuniverse extended with CT, which is then interpreted back to CZF+REA. A key benefit of the first way is that the theory CZF+REA_U+RDC also supports the intended set-theoretic interpretation of the extensional level of MFcind. Finally, all the theories considered, except mTTcind+AC+CT, are shown to be of the same proof-theoretic strength.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130545640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Limits of real numbers in the binary signed digit representation","authors":"Franziskus Wiesnet, Nils Köpp","doi":"10.46298/lmcs-18(3:24)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(3:24)2022","url":null,"abstract":"We extract verified algorithms for exact real number computation from\u0000constructive proofs. To this end we use a coinductive representation of reals\u0000as streams of binary signed digits. The main objective of this paper is the\u0000formalisation of a constructive proof that real numbers are closed with respect\u0000to limits. All the proofs of the main theorem and the first application are\u0000implemented in the Minlog proof system and the extracted terms are further\u0000translated into Haskell. We compare two approaches. The first approach is a\u0000direct proof. In the second approach we make use of the representation of reals\u0000by a Cauchy-sequence of rationals. Utilizing translations between the two\u0000represenation and using the completeness of the Cauchy-reals, the proof is very\u0000short. In both cases we use Minlog's program extraction mechanism to\u0000automatically extract a formally verified program that transforms a converging\u0000sequence of reals, i.e.~a sequence of streams of binary signed digits together\u0000with a modulus of convergence, into the binary signed digit representation of\u0000its limit. The correctness of the extracted terms follows directly from the\u0000soundness theorem of program extraction. As a first application we use the\u0000extracted algorithms together with Heron's method to construct an algorithm\u0000that computes square roots with respect to the binary signed digit\u0000representation. In a second application we use the convergence theorem to show\u0000that the signed digit representation of real numbers is closed under\u0000multiplication.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115125869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Converse extensionality and apartness","authors":"B. V. D. Berg, Robert Passmann","doi":"10.46298/lmcs-18(4:13)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(4:13)2022","url":null,"abstract":"In this paper we try to find a computational interpretation for a strong form\u0000of extensionality, which we call \"converse extensionality\". Converse\u0000extensionality principles, which arise as the Dialectica interpretation of the\u0000axiom of extensionality, were first studied by Howard. In order to give a\u0000computational interpretation to these principles, we reconsider Brouwer's\u0000apartness relation, a strong constructive form of inequality. Formally, we\u0000provide a categorical construction to endow every typed combinatory algebra\u0000with an apartness relation. We then exploit that functions reflect apartness,\u0000in addition to preserving equality, to prove that the resulting categories of\u0000assemblies model a converse extensionality principle.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123146823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Reduction Free Normalisation for a proof irrelevant type of propositions","authors":"T. Coquand","doi":"10.46298/lmcs-19(3:5)2023","DOIUrl":"https://doi.org/10.46298/lmcs-19(3:5)2023","url":null,"abstract":"We show normalisation and decidability of convertibility for a type theory\u0000with a hierarchy of universes and a proof irrelevant type of propositions,\u0000close to the type system used in the proof assistant Lean. Contrary to previous\u0000arguments, the proof does not require explicitly to introduce a notion of\u0000neutral and normal forms.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122694513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stashing And Parallelization Pentagons","authors":"V. Brattka","doi":"10.46298/lmcs-17(4:20)2021","DOIUrl":"https://doi.org/10.46298/lmcs-17(4:20)2021","url":null,"abstract":"Parallelization is an algebraic operation that lifts problems to sequences in\u0000a natural way. Given a sequence as an instance of the parallelized problem,\u0000another sequence is a solution of this problem if every component is\u0000instance-wise a solution of the original problem. In the Weihrauch lattice\u0000parallelization is a closure operator. Here we introduce a dual operation that\u0000we call stashing and that also lifts problems to sequences, but such that only\u0000some component has to be an instance-wise solution. In this case the solution\u0000is stashed away in the sequence. This operation, if properly defined, induces\u0000an interior operator in the Weihrauch lattice. We also study the action of the\u0000monoid induced by stashing and parallelization on the Weihrauch lattice, and we\u0000prove that it leads to at most five distinct degrees, which (in the maximal\u0000case) are always organized in pentagons. We also introduce another closely\u0000related interior operator in the Weihrauch lattice that replaces solutions of\u0000problems by upper Turing cones that are strong enough to compute solutions. It\u0000turns out that on parallelizable degrees this interior operator corresponds to\u0000stashing. This implies that, somewhat surprisingly, all problems which are\u0000simultaneously parallelizable and stashable have computability-theoretic\u0000characterizations. Finally, we apply all these results in order to study the\u0000recently introduced discontinuity problem, which appears as the bottom of a\u0000number of natural stashing-parallelization pentagons. The discontinuity problem\u0000is not only the stashing of several variants of the lesser limited principle of\u0000omniscience, but it also parallelizes to the non-computability problem. This\u0000supports the slogan that \"non-computability is the parallelization of\u0000discontinuity\".","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"190 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116517623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Massimo Bartoletti, J. Chiang, Alberto Lluch-Lafuente
{"title":"A theory of Automated Market Makers in DeFi","authors":"Massimo Bartoletti, J. Chiang, Alberto Lluch-Lafuente","doi":"10.46298/lmcs-18(4:12)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(4:12)2022","url":null,"abstract":"Automated market makers (AMMs) are one of the most prominent decentralized\u0000finance (DeFi) applications. AMMs allow users to trade different types of\u0000crypto-tokens, without the need to find a counter-party. There are several\u0000implementations and models for AMMs, featuring a variety of sophisticated\u0000economic mechanisms. We present a theory of AMMs. The core of our theory is an\u0000abstract operational model of the interactions between users and AMMs, which\u0000can be concretised by instantiating the economic mechanisms. We exploit our\u0000theory to formally prove a set of fundamental properties of AMMs,\u0000characterizing both structural and economic aspects. We do this by abstracting\u0000from the actual economic mechanisms used in implementations, and identifying\u0000sufficient conditions which ensure the relevant properties. Notably, we devise\u0000a general solution to the arbitrage problem, the main game-theoretic foundation\u0000behind the economic mechanisms of AMMs.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127602670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
L. Aceto, Valentina Castiglioni, A. Ingólfsdóttir, B. Luttik, Mathias R. Perdesen
{"title":"On the Axiomatisability of Parallel Composition","authors":"L. Aceto, Valentina Castiglioni, A. Ingólfsdóttir, B. Luttik, Mathias R. Perdesen","doi":"10.46298/lmcs-18(1:15)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(1:15)2022","url":null,"abstract":"This paper studies the existence of finite equational axiomatisations of the\u0000interleaving parallel composition operator modulo the behavioural equivalences\u0000in van Glabbeek's linear time-branching time spectrum. In the setting of the\u0000process algebra BCCSP over a finite set of actions, we provide finite,\u0000ground-complete axiomatisations for various simulation and (decorated) trace\u0000semantics. We also show that no congruence over BCCSP that includes\u0000bisimilarity and is included in possible futures equivalence has a finite,\u0000ground-complete axiomatisation; this negative result applies to all the nested\u0000trace and nested simulation semantics.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131623955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
