LIVIVO - The Search Portal for Life Sciences

zur deutschen Oberfläche wechseln
Advanced search

Search results

Result 1 - 7 of total 7

Search options

  1. Book ; Online: Leaderless Population Protocols Decide Double-exponential Thresholds

    Czerner, Philipp

    2022  

    Abstract: Population protocols are a model of distributed computation in which finite-state agents interact randomly in pairs. A protocol decides for any initial configuration whether it satisfies a fixed property, specified as a predicate on the set of ... ...

    Abstract Population protocols are a model of distributed computation in which finite-state agents interact randomly in pairs. A protocol decides for any initial configuration whether it satisfies a fixed property, specified as a predicate on the set of configurations. The state complexity of a predicate is smallest number of states of any protocol deciding that predicate. For threshold predicates of the form $x\ge k$, with $k$ constant, prior work has shown that they have state complexity $\Theta(\log\log k)$ if the protocol is extended with leaders. For ordinary protocols it is only known to be in $\Omega(\log\log k)\cap \mathcal{O}(\log k)$. We close this remaining gap by showing that it is $\Theta(\log\log k)$ as well, i.e. we construct protocols with $\mathcal{O}(n)$ states deciding $x\ge k$ with $k\ge2^{2^n}$.
    Keywords Computer Science - Distributed ; Parallel ; and Cluster Computing
    Publishing date 2022-04-05
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

    Full text online

    More links

    Kategorien

    Inter-library loan at ZB MED

    Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

  2. Book ; Online: A Resolution-Based Interactive Proof System for UNSAT

    Czerner, Philipp / Esparza, Javier / Krasotin, Valentin

    2024  

    Abstract: Modern SAT or QBF solvers are expected to produce correctness certificates. However, certificates have worst-case exponential size (unless $\textsf{NP}=\textsf{coNP}$), and at recent SAT competitions the largest certificates of unsatisfiability are ... ...

    Abstract Modern SAT or QBF solvers are expected to produce correctness certificates. However, certificates have worst-case exponential size (unless $\textsf{NP}=\textsf{coNP}$), and at recent SAT competitions the largest certificates of unsatisfiability are starting to reach terabyte size. Recently, Couillard, Czerner, Esparza, and Majumdar have suggested to replace certificates with interactive proof systems based on the $\textsf{IP}=\textsf{PSPACE}$ theorem. They have presented an interactive protocol between a prover and a verifier for an extension of QBF. The overall running time of the protocol is linear in the time needed by a standard BDD-based algorithm, and the time invested by the verifier is polynomial in the size of the formula. (So, in particular, the verifier never has to read or process exponentially long certificates). We call such an interactive protocol competitive with the BDD algorithm for solving QBF. While BDD-algorithms are state-of-the-art for certain classes of QBF instances, no modern (UN)SAT solver is based on BDDs. For this reason, we initiate the study of interactive certification for more practical SAT algorithms. In particular, we address the question whether interactive protocols can be competitive with some variant of resolution. We present two contributions. First, we prove a theorem that reduces the problem of finding competitive interactive protocols to finding an arithmetisation of formulas satisfying certain commutativity properties. (Arithmetisation is the fundamental technique underlying the $\textsf{IP}=\textsf{PSPACE}$ theorem.) Then, we apply the theorem to give the first interactive protocol for the Davis-Putnam resolution procedure.

    Comment: 21 pages
    Keywords Computer Science - Logic in Computer Science ; F.1.2 ; F.4.1
    Subject code 000
    Publishing date 2024-01-26
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

    Full text online

    More links

    Kategorien

    Inter-library loan at ZB MED

    Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

  3. Book ; Online: Making $\textsf{IP}=\textsf{PSPACE}$ Practical

    Couillard, Eszter / Czerner, Philipp / Esparza, Javier / Majumdar, Rupak

    Efficient Interactive Protocols for BDD Algorithms

    2023  

    Abstract: We show that interactive protocols between a prover and a verifier, a well-known tool of complexity theory, can be used in practice to certify the correctness of automated reasoning tools. Theoretically, interactive protocols exist for all $\textsf{ ... ...

    Abstract We show that interactive protocols between a prover and a verifier, a well-known tool of complexity theory, can be used in practice to certify the correctness of automated reasoning tools. Theoretically, interactive protocols exist for all $\textsf{PSPACE}$ problems. The verifier of a protocol checks the prover's answer to a problem instance in probabilistic polynomial time, with polynomially many bits of communication, and with exponentially small probability of error. (The prover may need exponential time.) Existing interactive protocols are not used in practice because their provers use naive algorithms, inefficient even for small instances, that are incompatible with practical implementations of automated reasoning. We bridge the gap between theory and practice by means of an interactive protocol whose prover uses BDDs. We consider the problem of counting the number of assignments to a QBF instance ($\#\textrm{CP}$), which has a natural BDD-based algorithm. We give an interactive protocol for $\#\textrm{CP}$ whose prover is implemented on top of an extended BDD library. The prover has only a linear overhead in computation time over the natural algorithm. We have implemented our protocol in $\textsf{blic}$, a certifying tool for $\#\textrm{CP}$. Experiments on standard QBF benchmarks show that $\textsf{blic}$ is competitive with state-of-the-art QBF-solvers. The run time of the verifier is negligible. While loss of absolute certainty can be concerning, the error probability in our experiments is at most $10^{-10}$ and reduces to $10^{-10k}$ by repeating the verification $k$ times.
    Keywords Computer Science - Logic in Computer Science ; Computer Science - Computational Complexity
    Subject code 000
    Publishing date 2023-05-19
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

    Full text online

    More links

    Kategorien

    Inter-library loan at ZB MED

    Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

  4. Book ; Online: Running Time Analysis of Broadcast Consensus Protocols

    Czerner, Philipp / Jaax, Stefan

    2021  

    Abstract: Broadcast consensus protocols (BCPs) are a model of computation, in which anonymous, identical, finite-state agents compute by sending/receiving global broadcasts. BCPs are known to compute all number predicates in $\mathsf{NL}=\mathsf{NSPACE}(\log n)$ ... ...

    Abstract Broadcast consensus protocols (BCPs) are a model of computation, in which anonymous, identical, finite-state agents compute by sending/receiving global broadcasts. BCPs are known to compute all number predicates in $\mathsf{NL}=\mathsf{NSPACE}(\log n)$ where $n$ is the number of agents. They can be considered an extension of the well-established model of population protocols. This paper investigates execution time characteristics of BCPs. We show that every predicate computable by population protocols is computable by a BCP with expected $\mathcal{O}(n \log n)$ interactions, which is asymptotically optimal. We further show that every log-space, randomized Turing machine can be simulated by a BCP with $\mathcal{O}(n \log n \cdot T)$ interactions in expectation, where $T$ is the expected runtime of the Turing machine. This allows us to characterise polynomial-time BCPs as computing exactly the number predicates in $\mathsf{ZPL}$, i.e. predicates decidable by log-space bounded randomised Turing machine with zero-error in expected polynomial time where the input is encoded as unary.

    Comment: To be published in the Proceedings of the 24th International Conference on Foundations of Software Science and Computation Structures (FoSSaCS), 2021
    Keywords Computer Science - Distributed ; Parallel ; and Cluster Computing
    Subject code 004 ; 005
    Publishing date 2021-01-11
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

    Full text online

    More links

    Kategorien

    Inter-library loan at ZB MED

    Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

  5. Book ; Online: Fast and Succinct Population Protocols for Presburger Arithmetic

    Czerner, Philipp / Guttenberg, Roland / Helfrich, Martin / Esparza, Javier

    2022  

    Abstract: In their 2006 seminal paper in Distributed Computing, Angluin et al. present a construction that, given any Presburger predicate as input, outputs a leaderless population protocol that decides the predicate. The protocol for a predicate of size $m$ (when ...

    Abstract In their 2006 seminal paper in Distributed Computing, Angluin et al. present a construction that, given any Presburger predicate as input, outputs a leaderless population protocol that decides the predicate. The protocol for a predicate of size $m$ (when expressed as a Boolean combination of threshold and remainder predicates with coefficients in binary) runs in $\mathcal{O}(m \cdot n^2 \log n)$ expected number of interactions, which is almost optimal in $n$. However, the number of states of the protocol is exponential in $m$. Blondin et al. described in STACS 2020 another construction that produces protocols with a polynomial number of states, but exponential expected number of interactions. We present a construction that produces protocols with $\mathcal{O}(m)$ states that run in expected $\mathcal{O}(m^{7} \cdot n^2)$ interactions, optimal in $n$, for all inputs of size $\Omega(m)$. For this we introduce population computers, a carefully crafted generalization of population protocols easier to program, and show that our computers for Presburger predicates can be translated into fast and succinct population protocols.

    Comment: 58 pages, 7 figures, to be published in the Journal of Computer and System Sciences, Special Issue on SAND 2022
    Keywords Computer Science - Distributed ; Parallel ; and Cluster Computing ; F.1.1
    Subject code 511
    Publishing date 2022-02-23
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

    Full text online

    More links

    Kategorien

    Inter-library loan at ZB MED

    Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

  6. Book ; Online: Compact Oblivious Routing in Weighted Graphs

    Czerner, Philipp / Räcke, Harald

    2020  

    Abstract: The space-requirement for routing-tables is an important characteristic of routing schemes. For the cost-measure of minimizing the total network load there exist a variety of results that show tradeoffs between stretch and required size for the routing ... ...

    Abstract The space-requirement for routing-tables is an important characteristic of routing schemes. For the cost-measure of minimizing the total network load there exist a variety of results that show tradeoffs between stretch and required size for the routing tables. This paper designs compact routing schemes for the cost-measure congestion, where the goal is to minimize the maximum relative load of a link in the network (the relative load of a link is its traffic divided by its bandwidth). We show that for arbitrary undirected graphs we can obtain oblivious routing strategies with competitive ratio $\tilde{\mathcal{O}}(1)$ that have header length $\tilde{\mathcal{O}}(1)$, label size $\tilde{\mathcal{O}}(1)$, and require routing-tables of size $\tilde{\mathcal{O}}(\operatorname{deg}(v))$ at each vertex $v$ in the graph. This improves a result of R\"acke and Schmid who proved a similar result in unweighted graphs.

    Comment: To be published in the Proceedings of the 28th European Symposium on Algorithms (ESA), 2020
    Keywords Computer Science - Networking and Internet Architecture
    Subject code 000
    Publishing date 2020-07-05
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

    Full text online

    More links

    Kategorien

    Inter-library loan at ZB MED

    Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

  7. Book ; Online: Lower Bounds on the State Complexity of Population Protocols

    Czerner, Philipp / Esparza, Javier / Leroux, Jérôme

    2021  

    Abstract: Population protocols are a model of computation in which an arbitrary number of indistinguishable finite-state agents interact in pairs. The goal of the agents is to decide by stable consensus whether their initial global configuration satisfies a given ... ...

    Abstract Population protocols are a model of computation in which an arbitrary number of indistinguishable finite-state agents interact in pairs. The goal of the agents is to decide by stable consensus whether their initial global configuration satisfies a given property, specified as a predicate on the set of configurations. The state complexity of a predicate is the number of states of a smallest protocol that computes it. Previous work by Blondin \textit{et al.} has shown that the counting predicates $x \geq \eta$ have state complexity $\mathcal{O}(\log \eta)$ for leaderless protocols and $\mathcal{O}(\log \log \eta)$ for protocols with leaders. We obtain the first non-trivial lower bounds: the state complexity of $x \geq \eta$ is $\Omega(\log\log \eta)$ for leaderless protocols, and the inverse of a non-elementary function for protocols with leaders.

    Comment: Journal version
    Keywords Computer Science - Distributed ; Parallel ; and Cluster Computing
    Subject code 005
    Publishing date 2021-02-23
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

    Full text online

    More links

    Kategorien

    Inter-library loan at ZB MED

    Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

To top