38,899 research outputs found
Tableaux for Policy Synthesis for MDPs with PCTL* Constraints
Markov decision processes (MDPs) are the standard formalism for modelling
sequential decision making in stochastic environments. Policy synthesis
addresses the problem of how to control or limit the decisions an agent makes
so that a given specification is met. In this paper we consider PCTL*, the
probabilistic counterpart of CTL*, as the specification language. Because in
general the policy synthesis problem for PCTL* is undecidable, we restrict to
policies whose execution history memory is finitely bounded a priori.
Surprisingly, no algorithm for policy synthesis for this natural and
expressive framework has been developed so far. We close this gap and describe
a tableau-based algorithm that, given an MDP and a PCTL* specification, derives
in a non-deterministic way a system of (possibly nonlinear) equalities and
inequalities. The solutions of this system, if any, describe the desired
(stochastic) policies.
Our main result in this paper is the correctness of our method, i.e.,
soundness, completeness and termination.Comment: This is a long version of a conference paper published at TABLEAUX
2017. It contains proofs of the main results and fixes a bug. See the
footnote on page 1 for detail
Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions
We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each face of this polytope. We can subsequently obtain various relations, such as transformations and three-term relations, of these functions by considering geometrical properties of this polytope. The most general functions we describe in this way are sums of two very-well-poised _10φ_9's and their Nassrallah-Rahman type integral representation
Inherent Limitations of Hybrid Transactional Memory
Several Hybrid Transactional Memory (HyTM) schemes have recently been
proposed to complement the fast, but best-effort, nature of Hardware
Transactional Memory (HTM) with a slow, reliable software backup. However, the
fundamental limitations of building a HyTM with nontrivial concurrency between
hardware and software transactions are still not well understood.
In this paper, we propose a general model for HyTM implementations, which
captures the ability of hardware transactions to buffer memory accesses, and
allows us to formally quantify and analyze the amount of overhead
(instrumentation) of a HyTM scheme. We prove the following: (1) it is
impossible to build a strictly serializable HyTM implementation that has both
uninstrumented reads and writes, even for weak progress guarantees, and (2)
under reasonable assumptions, in any opaque progressive HyTM, a hardware
transaction must incur instrumentation costs linear in the size of its data
set. We further provide two upper bound implementations whose instrumentation
costs are optimal with respect to their progress guarantees. In sum, this paper
captures for the first time an inherent trade-off between the degree of
concurrency a HyTM provides between hardware and software transactions, and the
amount of instrumentation overhead the implementation must incur
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