2,520 research outputs found
Feasible Automata for Two-Variable Logic with Successor on Data Words
We introduce an automata model for data words, that is words that carry at
each position a symbol from a finite alphabet and a value from an unbounded
data domain. The model is (semantically) a restriction of data automata,
introduced by Bojanczyk, et. al. in 2006, therefore it is called weak data
automata. It is strictly less expressive than data automata and the expressive
power is incomparable with register automata. The expressive power of weak data
automata corresponds exactly to existential monadic second order logic with
successor +1 and data value equality \sim, EMSO2(+1,\sim). It follows from
previous work, David, et. al. in 2010, that the nonemptiness problem for weak
data automata can be decided in 2-NEXPTIME. Furthermore, we study weak B\"uchi
automata on data omega-strings. They can be characterized by the extension of
EMSO2(+1,\sim) with existential quantifiers for infinite sets. Finally, the
same complexity bound for its nonemptiness problem is established by a
nondeterministic polynomial time reduction to the nonemptiness problem of weak
data automata.Comment: 21 page
Learning Markov Decision Processes for Model Checking
Constructing an accurate system model for formal model verification can be
both resource demanding and time-consuming. To alleviate this shortcoming,
algorithms have been proposed for automatically learning system models based on
observed system behaviors. In this paper we extend the algorithm on learning
probabilistic automata to reactive systems, where the observed system behavior
is in the form of alternating sequences of inputs and outputs. We propose an
algorithm for automatically learning a deterministic labeled Markov decision
process model from the observed behavior of a reactive system. The proposed
learning algorithm is adapted from algorithms for learning deterministic
probabilistic finite automata, and extended to include both probabilistic and
nondeterministic transitions. The algorithm is empirically analyzed and
evaluated by learning system models of slot machines. The evaluation is
performed by analyzing the probabilistic linear temporal logic properties of
the system as well as by analyzing the schedulers, in particular the optimal
schedulers, induced by the learned models.Comment: In Proceedings QFM 2012, arXiv:1212.345
High-level Counterexamples for Probabilistic Automata
Providing compact and understandable counterexamples for violated system
properties is an essential task in model checking. Existing works on
counterexamples for probabilistic systems so far computed either a large set of
system runs or a subset of the system's states, both of which are of limited
use in manual debugging. Many probabilistic systems are described in a guarded
command language like the one used by the popular model checker PRISM. In this
paper we describe how a smallest possible subset of the commands can be
identified which together make the system erroneous. We additionally show how
the selected commands can be further simplified to obtain a well-understandable
counterexample
Complexity of Restricted and Unrestricted Models of Molecular Computation
In [9] and [2] a formal model for molecular computing was
proposed, which makes focused use of affinity purification.
The use of PCR was suggested to expand the range of
feasible computations, resulting in a second model. In this
note, we give a precise characterization of these two models
in terms of recognized computational complexity classes,
namely branching programs (BP) and nondeterministic
branching programs (NBP) respectively. This allows us to
give upper and lower bounds on the complexity of desired
computations. Examples are given of computable and
uncomputable problems, given limited time
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