80 research outputs found
Sampled Semantics of Timed Automata
Sampled semantics of timed automata is a finite approximation of their dense
time behavior. While the former is closer to the actual software or hardware
systems with a fixed granularity of time, the abstract character of the latter
makes it appealing for system modeling and verification. We study one aspect of
the relation between these two semantics, namely checking whether the system
exhibits some qualitative (untimed) behaviors in the dense time which cannot be
reproduced by any implementation with a fixed sampling rate. More formally, the
\emph{sampling problem} is to decide whether there is a sampling rate such that
all qualitative behaviors (the untimed language) accepted by a given timed
automaton in dense time semantics can be also accepted in sampled semantics. We
show that this problem is decidable
Infinite Networks, Halting and Local Algorithms
The immediate past has witnessed an increased amount of interest in local
algorithms, i.e., constant time distributed algorithms. In a recent survey of
the topic (Suomela, ACM Computing Surveys, 2013), it is argued that local
algorithms provide a natural framework that could be used in order to
theoretically control infinite networks in finite time. We study a
comprehensive collection of distributed computing models and prove that if
infinite networks are included in the class of structures investigated, then
every universally halting distributed algorithm is in fact a local algorithm.
To contrast this result, we show that if only finite networks are allowed, then
even very weak distributed computing models can define nonlocal algorithms that
halt everywhere. The investigations in this article continue the studies in the
intersection of logic and distributed computing initiated in (Hella et al.,
PODC 2012) and (Kuusisto, CSL 2013).Comment: In Proceedings GandALF 2014, arXiv:1408.556
Regular Cost Functions, Part I: Logic and Algebra over Words
The theory of regular cost functions is a quantitative extension to the
classical notion of regularity. A cost function associates to each input a
non-negative integer value (or infinity), as opposed to languages which only
associate to each input the two values "inside" and "outside". This theory is a
continuation of the works on distance automata and similar models. These models
of automata have been successfully used for solving the star-height problem,
the finite power property, the finite substitution problem, the relative
inclusion star-height problem and the boundedness problem for monadic-second
order logic over words. Our notion of regularity can be -- as in the classical
theory of regular languages -- equivalently defined in terms of automata,
expressions, algebraic recognisability, and by a variant of the monadic
second-order logic. These equivalences are strict extensions of the
corresponding classical results. The present paper introduces the cost monadic
logic, the quantitative extension to the notion of monadic second-order logic
we use, and show that some problems of existence of bounds are decidable for
this logic. This is achieved by introducing the corresponding algebraic
formalism: stabilisation monoids.Comment: 47 page
Decentralized Hybrid Formation Control of Unmanned Aerial Vehicles
This paper presents a decentralized hybrid supervisory control approach for a
team of unmanned helicopters that are involved in a leader-follower formation
mission. Using a polar partitioning technique, the motion dynamics of the
follower helicopters are abstracted to finite state machines. Then, a discrete
supervisor is designed in a modular way for different components of the
formation mission including reaching the formation, keeping the formation, and
collision avoidance. Furthermore, a formal technique is developed to design the
local supervisors decentralizedly, so that the team of helicopters as whole,
can cooperatively accomplish a collision-free formation task
On Matrices, Automata, and Double Counting
Matrix models are ubiquitous for constraint problems. Many such problems have a matrix of variables M, with the same constraint defined by a finite-state automaton A on each row of M and a global cardinality constraint gcc on each column of M. We give two methods for deriving, by double counting,
necessary conditions on the cardinality variables of the gcc constraints from the automaton A. The first method yields linear necessary conditions and simple arithmetic constraints. The second method introduces the cardinality automaton, which abstracts the overall behaviour of all the row automata and can be encoded by a set of linear constraints. We evaluate the impact of our methods on a large set of nurse rostering problem instances
State-deterministic Finite Automata with Translucent Letters and Finite Automata with Nondeterministically Translucent Letters
Deterministic and nondeterministic finite automata with translucent letters
were introduced by Nagy and Otto more than a decade ago as Cooperative
Distributed systems of a kind of stateless restarting automata with window size
one. These finite state machines have a surprisingly large expressive power:
all commutative semi-linear languages and all rational trace languages can be
accepted by them including various not context-free languages. While the
nondeterministic variant defines a language class with nice closure properties,
the deterministic variant is weaker, however it contains all regular languages,
some non-regular context-free languages, as the Dyck language, and also some
languages that are not even context-free. In all those models for each state,
the letters of the alphabet could be in one of the following categories: the
automaton cannot see the letter (it is translucent), there is a transition
defined on the letter (maybe more than one transitions in nondeterministic
case) or none of the above categories (the automaton gets stuck by seeing this
letter at the given state and this computation is not accepting).
State-deterministic automata are recent models, where the next state of the
computation determined by the structure of the automata and it is independent
of the processed letters. In this paper our aim is twofold, on the one hand, we
investigate state-deterministic finite automata with translucent letters. These
automata are specially restricted deterministic finite automata with
translucent letters.
In the other novel model we present, it is allowed that for a state the set
of translucent letters and the set of letters for which transition is defined
are not disjoint. One can interpret this fact that the automaton has a
nondeterministic choice for each occurrence of such letters to see them (and
then erase and make the transition) or not to see that occurrence at that time.
Based on these semi-translucent letters, the expressive power of the automata
increases, i.e., in this way a proper generalization of the previous models is
obtained.Comment: In Proceedings AFL 2023, arXiv:2309.0112
Uniform Random Sampling of Traces in Very Large Models
This paper presents some first results on how to perform uniform random walks
(where every trace has the same probability to occur) in very large models. The
models considered here are described in a succinct way as a set of
communicating reactive modules. The method relies upon techniques for counting
and drawing uniformly at random words in regular languages. Each module is
considered as an automaton defining such a language. It is shown how it is
possible to combine local uniform drawings of traces, and to obtain some global
uniform random sampling, without construction of the global model
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