5,725 research outputs found
Size-Change Abstraction and Max-Plus Automata
Max-plus automata (over ℕ ∪ − ∞) are finite devices that map input words to non-negative integers or − ∞. In this paper we present (a) an algorithm allowing to compute the asymptotic behaviour of max-plus automata, and (b) an application of this technique to the evaluation of the computational time complexity of programs
Unambiguous Separators for Tropical Tree Automata
In this paper we show that given a max-plus automaton (over trees, and with real weights) computing a function f and a min-plus automaton (similar) computing a function g such that f ? g, there exists effectively an unambiguous tropical automaton computing h such that f ? h ? g.
This generalizes a result of Lombardy and Mairesse of 2006 stating that series which are both max-plus and min-plus rational are unambiguous. This generalization goes in two directions: trees are considered instead of words, and separation is established instead of characterization (separation implies characterization). The techniques in the two proofs are very different
Performance Evaluation of Components Using a Granularity-based Interface Between Real-Time Calculus and Timed Automata
To analyze complex and heterogeneous real-time embedded systems, recent works
have proposed interface techniques between real-time calculus (RTC) and timed
automata (TA), in order to take advantage of the strengths of each technique
for analyzing various components. But the time to analyze a state-based
component modeled by TA may be prohibitively high, due to the state space
explosion problem. In this paper, we propose a framework of granularity-based
interfacing to speed up the analysis of a TA modeled component. First, we
abstract fine models to work with event streams at coarse granularity. We
perform analysis of the component at multiple coarse granularities and then
based on RTC theory, we derive lower and upper bounds on arrival patterns of
the fine output streams using the causality closure algorithm. Our framework
can help to achieve tradeoffs between precision and analysis time.Comment: QAPL 201
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Containment and equivalence of weighted automata: Probabilistic and max-plus cases
This paper surveys some results regarding decision problems for probabilistic and max-plus automata, such as containment and equivalence. Probabilistic and max-plus automata are part of the general family of weighted automata, whose semantics are maps from words to real values. Given two weighted automata, the equivalence problem asks whether their semantics are the same, and the containment problem whether one is point-wise smaller than the other one. These problems have been studied intensively and this paper will review some techniques used to show (un)decidability and state a list of open questions that still remain
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Comparison of max-plus automata and joint spectral radius of tropical matrices
Weighted automata over the max-plus semiring S are closely related to finitely generated semigroups of matrices over S. In this paper, we use results in automata theory to study two quantities associated with sets of matrices: the joint spectral radius and the ultimate rank. We prove that these two quantities are not computable over the tropical semiring, i.e. there is no algorithm that takes as input a finite set of matrices M and provides as output the joint spectral radius (resp. the ultimate rank) of M. On the other hand, we prove that the joint spectral radius is nevertheless approximable and we exhibit restricted cases in which the joint spectral radius and the ultimate rank are computable. To reach this aim, we study the problem of comparing functions computed by weighted automata over the tropical semiring. This problem is known to be undecidable and we prove that it remains undecidable in some specific subclasses of automata
Pushdown Control-Flow Analysis of Higher-Order Programs
Context-free approaches to static analysis gain precision over classical
approaches by perfectly matching returns to call sites---a property that
eliminates spurious interprocedural paths. Vardoulakis and Shivers's recent
formulation of CFA2 showed that it is possible (if expensive) to apply
context-free methods to higher-order languages and gain the same boost in
precision achieved over first-order programs.
To this young body of work on context-free analysis of higher-order programs,
we contribute a pushdown control-flow analysis framework, which we derive as an
abstract interpretation of a CESK machine with an unbounded stack. One
instantiation of this framework marks the first polyvariant pushdown analysis
of higher-order programs; another marks the first polynomial-time analysis. In
the end, we arrive at a framework for control-flow analysis that can
efficiently compute pushdown generalizations of classical control-flow
analyses.Comment: The 2010 Workshop on Scheme and Functional Programmin
Explicit Model Checking of Very Large MDP using Partitioning and Secondary Storage
The applicability of model checking is hindered by the state space explosion
problem in combination with limited amounts of main memory. To extend its
reach, the large available capacities of secondary storage such as hard disks
can be exploited. Due to the specific performance characteristics of secondary
storage technologies, specialised algorithms are required. In this paper, we
present a technique to use secondary storage for probabilistic model checking
of Markov decision processes. It combines state space exploration based on
partitioning with a block-iterative variant of value iteration over the same
partitions for the analysis of probabilistic reachability and expected-reward
properties. A sparse matrix-like representation is used to store partitions on
secondary storage in a compact format. All file accesses are sequential, and
compression can be used without affecting runtime. The technique has been
implemented within the Modest Toolset. We evaluate its performance on several
benchmark models of up to 3.5 billion states. In the analysis of time-bounded
properties on real-time models, our method neutralises the state space
explosion induced by the time bound in its entirety.Comment: The final publication is available at Springer via
http://dx.doi.org/10.1007/978-3-319-24953-7_1
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