1,594 research outputs found
Are Lock-Free Concurrent Algorithms Practically Wait-Free?
Lock-free concurrent algorithms guarantee that some concurrent operation will
always make progress in a finite number of steps. Yet programmers prefer to
treat concurrent code as if it were wait-free, guaranteeing that all operations
always make progress. Unfortunately, designing wait-free algorithms is
generally a very complex task, and the resulting algorithms are not always
efficient. While obtaining efficient wait-free algorithms has been a long-time
goal for the theory community, most non-blocking commercial code is only
lock-free.
This paper suggests a simple solution to this problem. We show that, for a
large class of lock- free algorithms, under scheduling conditions which
approximate those found in commercial hardware architectures, lock-free
algorithms behave as if they are wait-free. In other words, programmers can
keep on designing simple lock-free algorithms instead of complex wait-free
ones, and in practice, they will get wait-free progress.
Our main contribution is a new way of analyzing a general class of lock-free
algorithms under a stochastic scheduler. Our analysis relates the individual
performance of processes with the global performance of the system using Markov
chain lifting between a complex per-process chain and a simpler system progress
chain. We show that lock-free algorithms are not only wait-free with
probability 1, but that in fact a general subset of lock-free algorithms can be
closely bounded in terms of the average number of steps required until an
operation completes.
To the best of our knowledge, this is the first attempt to analyze progress
conditions, typically stated in relation to a worst case adversary, in a
stochastic model capturing their expected asymptotic behavior.Comment: 25 page
Critical probabilities and convergence time of Percolation Probabilistic Cellular Automata
This paper considers a class of probabilistic cellular automata undergoing a
phase transition with an absorbing state. Denoting by the
neighbourhood of site , the transition probability is if or
otherwise, . For any there exists a
non-trivial critical probability that separates a phase
with an absorbing state from a fluctuating phase. This paper studies how the
neighbourhood affects the value of and provides lower
bounds for . Furthermore, by using dynamic renormalization
techniques, we prove that the expected convergence time of the processes on a
finite space with periodic boundaries grows exponentially (resp.
logarithmically) with the system size if (resp. ). This
provides a partial answer to an open problem in Toom et al. (1990, 1994).Comment: 50 pages, 19 Figure
Recurrence and Transience for Probabilistic Automata
In a context of -regular specifications for infinite execution
sequences, the classical B"uchi condition, or repeated liveness
condition, asks that an accepting state is visited infinitely often. In
this paper, we show that in a probabilistic context it is relevant to
strengthen this infinitely often condition. An execution path is now
accepting if the emph{proportion} of time spent on an accepting state
does not go to zero as the length of the path goes to infinity. We
introduce associated notions of recurrence and transience for
non-homogeneous finite Markov chains and study the computational
complexity of the associated problems. As Probabilistic B"uchi Automata
(PBA) have been an attempt to generalize B"uchi automata to a
probabilistic context, we define a class of Constrained Probabilistic
Automata with our new accepting condition on runs. The accepted language
is defined by the requirement that the measure of the set of accepting
runs is positive (probable semantics) or equals 1 (almost-sure
semantics). In contrast to the PBA case, we prove that
the emptiness problem for the language of a constrained probabilistic
B"uchi automaton with the probable semantics is decidable
Probabilistic propositional temporal logics
We present two (closely-related) propositional probabilistic temporal logics based on temporal logics of branching time as introduced by Ben-Ari, Pnueli, and Manna (Acta Inform. 20 (1983), 207–226), Emerson and Halpern (“Proceedings, 14th ACM Sympos. Theory of Comput.,” 1982, pp. 169–179, and Emerson and Clarke (Sci. Comput. Program. 2 (1982), 241–266). The first logic, PTLf, is interpreted over finite models, while the second logic, PTLb, which is an extension of the first one, is interpreted over infinite models with transition probabilities bounded away from 0. The logic PTLf allows us to reason about finite-state sequential probabilistic programs, and the logic PTLb allows us to reason about (finite-state) concurrent probabilistic programs, without any explicit reference to the actual values of their state-transition probabilities. A generalization of the tableau method yields deterministic single-exponential time decision procedures for our logics, and complete axiomatizations of them are given. Several meta-results, including the absence of a finite-model property for PTLb, and the connection between satisfiable formulae of PTLb and finite state concurrent probabilistic programs, are also discussed
Model Checking CSL for Markov Population Models
Markov population models (MPMs) are a widely used modelling formalism in the
area of computational biology and related areas. The semantics of a MPM is an
infinite-state continuous-time Markov chain. In this paper, we use the
established continuous stochastic logic (CSL) to express properties of Markov
population models. This allows us to express important measures of biological
systems, such as probabilistic reachability, survivability, oscillations,
switching times between attractor regions, and various others. Because of the
infinite state space, available analysis techniques only apply to a very
restricted subset of CSL properties. We present a full algorithm for model
checking CSL for MPMs, and provide experimental evidence showing that our
method is effective.Comment: In Proceedings QAPL 2014, arXiv:1406.156
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