Computation in networks of passively mobile finite-state sensors

Angluin, Dana; Aspnes, James; Diamadi, Zoë; Fischer, Michael J.; Peralta, René

doi:10.1007/s00446-005-0138-3

Cited by 475 publications

(707 citation statements)

References 22 publications

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“…We require the following theorem, due to Angluin, Aspnes, Diamadi, Fischer, and René [1], which states that any semilinear predicate can be decided by a CRD in expected time O ( n log n ). (This was subsequently reduced to O ( n ) by Angluin, Aspnes, and Eisenstat [3], but O ( n log n ) suffices for our purpose.…”

Section: Deterministic Computation Of Semilinear Functions In O(∥x∥mentioning

confidence: 99%

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Deterministic function computation with chemical reaction networks

2013

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Chemical reaction networks (CRNs) formally model chemistry in a well-mixed solution. CRNs are widely used to describe information processing occurring in natural cellular regulatory networks, and with upcoming advances in synthetic biology, CRNs are a promising language for the design of artificial molecular control circuitry. Nonetheless, despite the widespread use of CRNs in the natural sciences, the range of computational behaviors exhibited by CRNs is not well understood. CRNs have been shown to be efficiently Turing-universal (i.e., able to simulate arbitrary algorithms) when allowing for a small probability of error. CRNs that are guaranteed to converge on a correct answer, on the other hand, have been shown to decide only the semilinear predicates (a multi-dimensional generalization of “eventually periodic” sets). We introduce the notion of function, rather than predicate, computation by representing the output of a function f : ℕk → ℕl by a count of some molecular species, i.e., if the CRN starts with x1, …, xk molecules of some “input” species X1, …, Xk, the CRN is guaranteed to converge to having f(x1, …, xk) molecules of the “output” species Y1, …, Yl. We show that a function f : ℕk → ℕl is deterministically computed by a CRN if and only if its graph {(x, y) ∈ ℕk × ℕl ∣ f(x) = y} is a semilinear set. Finally, we show that each semilinear function f (a function whose graph is a semilinear set) can be computed by a CRN on input x in expected time O(polylog ∥x∥1).

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Section: Deterministic Computation Of Semilinear Functions In O(∥x∥mentioning

confidence: 99%

“…The importance of the model is underscored by the fact that equivalent models repeatedly arise in theoretical computer science under different guises: e.g. vector addition systems [16], petri nets [20], population protocols [1]. …”

Section: Introductionmentioning

confidence: 99%

Deterministic function computation with chemical reaction networks

2013

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“…There is a formal sense in which chemical reaction networks have been shown to be able to compute functions f : N k → N [8] and predicates N k → {0, 1} [4]. A function/predicate can be computed "deterministically" (i.e., regardless of the order in which reactions occur) ⇐⇒ it is semilinear (see [20] for a definition).…”

Section: Open Problemsmentioning

confidence: 99%

Computational Complexity of Atomic Chemical Reaction Networks

Doty

Zhu

2017

SOFSEM 2018: Theory and Practice of Computer Science

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Abstract. Informally, a chemical reaction network is "atomic" if each reaction may be interpreted as the rearrangement of indivisible units of matter. There are several reasonable definitions formalizing this idea. We investigate the computational complexity of deciding whether a given network is atomic according to each of these definitions. Primitive atomic, which requires each reaction to preserve the total number of atoms, is shown to be equivalent to mass conservation. Since it is known that it can be decided in polynomial time whether a given chemical reaction network is mass-conserving [32], the equivalence we show gives an efficient algorithm to decide primitive atomicity. Subset atomic further requires all atoms be species. We show that deciding if a network is subset atomic is in NP, and "whether a network is subset atomic with respect to a given atom set" is strongly NP-complete. Reachably atomic, studied by Adleman, Gopalkrishnan et al. [1, 23], further requires that each species has a sequence of reactions splitting it into its constituent atoms. Using a combinatorial argument, we show that there is a polynomial-time algorithm to decide whether a given network is reachably atomic, improving upon the result of Adleman et al. that the problem is decidable. We show that the reachability problem for reachably atomic networks is PSPACE-complete. Finally, we demonstrate equivalence relationships between our definitions and some cases of an existing definition of atomicity due to Gnacadja [21].

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“…As an example, some peer-to-peer file-sharing systems assume the peers are anonymous [12]. In the same vein, not all the sensor networks assume that each sensor has a proper identity [2,18].…”

Section: Introductionmentioning

confidence: 99%

Anonymous Asynchronous Systems: The Case of Failure Detectors

Bonnet

Raynal

2010

Lecture Notes in Computer Science

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Due the multiplicity of loci of control, a main issue distributed systems have to cope with lies in the uncertainty on the system state created by the adversaries that are asynchrony, failures, dynamicity, mobility, etc. Considering message-passing systems, this paper considers the uncertainty created by the net effect of three of these adversaries, namely, asynchrony, failures, and anonymity. This means that, in addition to be asynchronous and crash-prone, the processes have no identity.Trivially, agreement problems (e.g., consensus) that cannot be solved in presence of asynchrony and failures cannot be solved either when adding anonymity. The paper consequently proposes anonymous failure detectors to circumvent these impossibilities. It has several contributions. First it presents three classes of failure detectors (denoted AP , AΩ and AΣ) and show that they are the anonymous counterparts of the classes of perfect failure detectors, eventual leader failure detectors and quorum failure detectors, respectively. The class AΣ is new and showing it is the anonymous counterpart of the class Σ is not trivial. Then, the paper presents and proves correct a genuinely anonymous consensus algorithm based on the pair of anonymous failure detector classes (AΩ, AΣ) ("genuinely" means that, not only processes have no identity, but no process is aware of the total number of processes). This new algorithm is not a "straightforward extension" of an algorithm designed for non-anonymous systems. To benefit from AΣ, it uses a novel message exchange pattern where each phase of every round is made up of sub-rounds in which appropriate control information is exchanged. Finally, the paper discusses the notions of failure detector class hierarchy and weakest failure detector class for a given problem in the context of anonymous systems.

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Computation in networks of passively mobile finite-state sensors

Cited by 475 publications

References 22 publications

Deterministic function computation with chemical reaction networks

Deterministic function computation with chemical reaction networks

Computational Complexity of Atomic Chemical Reaction Networks

Anonymous Asynchronous Systems: The Case of Failure Detectors

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