Weak models of distributed computing, with connections to modal logic

Hella, Lauri; Järvisalo, Matti; Kuusisto, Antti; Laurinharju, Juhana; Lempiäinen, Tuomo; Luosto, Kerkko; Suomela, Jukka; Virtema, Jonni

doi:10.1007/s00446-013-0202-3

Cited by 37 publications

(55 citation statements)

References 49 publications

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“…The proof of Theorem 4.3 makes a crucial use of logic, thereby extending the work initiated in [8,9] and developed further in [11]. The articles [8,9,11] extend the scope of descriptive complexity theory (see [7,10,12]) to the realm of distributed computing by identifying a highly canonical oneto-one link between local algorithms and formulae of modal logic. This link is based on the novel idea of directly identifying Kripke models and distributed communication networks with each other.…”

Section: Introductionmentioning

confidence: 97%

“…The widely studied port-numbering model (see [2,8,9]) of distributed computing can be directly extended to a framework that contains infinite structures in addition to finite ones. In the port-numbering model, a node of degree k ≤ n, where n is a globally known finite degree bound, receives messages through k input ports and sends messages through k output ports.…”

Section: Introductionmentioning

confidence: 99%

“…Below we define a general distributed computing model based on relational structures and synchronized message passing automata. The port-numbering model VV c of [8,9] and all its subclasses can be directly simulated in our framework by restricting attention to suitable classes of structures and automata. We establish (Theorem 4.3 ) that if H is a class of communication networks definable by a first-order theory, then all universally halting algorithms over H are local algorithms.…”

Section: Introductionmentioning

confidence: 99%

“…For example, the classes of networks for the VV c model are easily seen to be definable by first-order formulae, as long as infinite structures are allowed. In fact, when the requirement of finiteness is lifted, all classes of structures in the comprehensive study in [8,9] can easily be seen to be first-order definable.…”

Section: Introductionmentioning

confidence: 99%

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Infinite Networks, Halting and Local Algorithms

Kuusisto¹

2014

Electron. Proc. Theor. Comput. Sci.

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The immediate past has witnessed an increased amount of interest in local algorithms, i.e., constant time distributed algorithms. In a recent survey of the topic (Suomela, ACM Computing Surveys, 2013), it is argued that local algorithms provide a natural framework that could be used in order to theoretically control infinite networks in finite time. We study a comprehensive collection of distributed computing models and prove that if infinite networks are included in the class of structures investigated, then every universally halting distributed algorithm is in fact a local algorithm. To contrast this result, we show that if only finite networks are allowed, then even very weak distributed computing models can define nonlocal algorithms that halt everywhere. The investigations in this article continue the studies in the intersection of logic and distributed computing initiated in (Hella et al., PODC 2012) and (Kuusisto, CSL 2013).Comment: In Proceedings GandALF 2014, arXiv:1408.556

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Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Infinite Networks, Halting and Local Algorithms

Kuusisto¹

2014

Electron. Proc. Theor. Comput. Sci.

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“…As the above equivalences are all effective, we can immediately settle the decidability question of the emptiness problem for local automata: it is decidable for the basic variant of [3,4], but undecidable for the extension considered in [9]. This is because the (finite) satisfiability problem is PSPACE-complete for basic modal logic but undecidable for MSO.…”

Section: Introductionmentioning

confidence: 98%

Emptiness Problems for Distributed Automata

Kuusisto

Reiter

2017

Electron. Proc. Theor. Comput. Sci.

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We investigate the decidability of the emptiness problem for three classes of distributed automata. These devices operate on finite directed graphs, acting as networks of identical finite-state machines that communicate in an infinite sequence of synchronous rounds. The problem is shown to be decidable in LOGSPACE for a class of forgetful automata, where the nodes see the messages received from their neighbors but cannot remember their own state. When restricted to the appropriate families of graphs, these forgetful automata are equivalent to classical finite word automata, but strictly more expressive than finite tree automata. On the other hand, we also show that the emptiness problem is undecidable in general. This already holds for two heavily restricted classes of distributed automata: those that reject immediately if they receive more than one message per round, and those whose state diagram must be acyclic except for self-loops.

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Identifiers in Registers

Bollig

Bouyer

Reiter

2019

Lecture Notes in Computer Science

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We propose a formal model of distributed computing based on register automata that captures a broad class of synchronous network algorithms. The local memory of each process is represented by a finitestate controller and a fixed number of registers, each of which can store the unique identifier of some process in the network. To underline the naturalness of our model, we show that it has the same expressive power as a certain extension of first-order logic on graphs whose nodes are equipped with a total order. Said extension lets us define new functions on the set of nodes by means of a so-called partial fixpoint operator. In spirit, our result bears close resemblance to a classical theorem of descriptive complexity theory that characterizes the complexity class pspace in terms of partial fixpoint logic (a proper superclass of the logic we consider here).

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Weak models of distributed computing, with connections to modal logic

Cited by 37 publications

References 49 publications

Infinite Networks, Halting and Local Algorithms

Infinite Networks, Halting and Local Algorithms

Emptiness Problems for Distributed Automata

Identifiers in Registers

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