47,868 research outputs found
Adaptable transition systems
We present an essential model of adaptable transition systems inspired by white-box approaches to adaptation and based on foundational models of component based systems. The key feature of adaptable transition systems are control propositions, imposing a clear separation between ordinary, functional behaviours and adaptive ones. We instantiate our approach on interface automata yielding adaptable interface automata, but it may be instantiated on other foundational models of component-based systems as well. We discuss how control propositions can be exploited in the specification and analysis of adaptive systems, focusing on various notions proposed in the literature, like adaptability, control loops, and control synthesis
Higher Dimensional Transition Systems
We introduce the notion of higher dimensional transition systems as a model of concurrency providing an elementary, set-theoretic formalisation of the idea of higher dimensional transition. We show an embedding of the category of higher dimensional transition systems into that of higher dimensional automata which cuts down to an equivalence when we restrict to non-degenerate automata. Moreover, we prove that the natural notion of bisimulation for such structures is a generalisation of the strong history preserving bisimulation, and provide an abstract categorical account of it via open maps. Finally, we define a notion of unfolding for higher dimensional transition systems and characterise the structures so obtained as a generalisation of event structures
Generalized Asynchronous Systems
The paper is devoted to a mathematical model of concurrency the special case
of which is asynchronous system. Distributed asynchronous automata are
introduced here. It is proved that the Petri nets and transition systems with
independence can be considered like the distributed asynchronous automata. Time
distributed asynchronous automata are defined in standard way by the map which
assigns time intervals to events. It is proved that the time distributed
asynchronous automata are generalized the time Petri nets and asynchronous
systems.Comment: 8 page
Building Squares with Optimal State Complexity in Restricted Active Self-Assembly
Tile Automata is a recently defined model of self-assembly that borrows many concepts from cellular automata to create active self-assembling systems where changes may be occurring within an assembly without requiring attachment. This model has been shown to be powerful, but many fundamental questions have yet to be explored. Here, we study the state complexity of assembling n Ă n squares in seeded Tile Automata systems where growth starts from a seed and tiles may attach one at a time, similar to the abstract Tile Assembly Model. We provide optimal bounds for three classes of seeded Tile Automata systems (all without detachment), which vary in the amount of complexity allowed in the transition rules. We show that, in general, seeded Tile Automata systems require Î(log^{1/4} n) states. For Single-Transition systems, where only one state may change in a transition rule, we show a bound of Î(log^{1/3} n), and for deterministic systems, where each pair of states may only have one associated transition rule, a bound of Î(({log n}/{log log n})^{1/2})
Coalgebra Learning via Duality
Automata learning is a popular technique for inferring minimal automata
through membership and equivalence queries. In this paper, we generalise
learning to the theory of coalgebras. The approach relies on the use of logical
formulas as tests, based on a dual adjunction between states and logical
theories. This allows us to learn, e.g., labelled transition systems, using
Hennessy-Milner logic. Our main contribution is an abstract learning algorithm,
together with a proof of correctness and termination
Building Squares with Optimal State Complexity in Restricted Active Self-Assembly
Tile Automata is a recently defined model of self-assembly that borrows many concepts from cellular automata to create active self-assembling systems where changes may be occurring within an assembly without requiring attachment. This model has been shown to be powerful, but many fundamental questions have yet to be explored. Here, we study the state complexity of assembling n Ă n squares in seeded Tile Automata systems where growth starts from a seed and tiles may attach one at a time, similar to the abstract Tile Assembly Model. We provide optimal bounds for three classes of seeded Tile Automata systems (all without detachment), which vary in the amount of complexity allowed in the transition rules. We show that, in general, seeded Tile Automata systems require Î(log^{1/4} n) states. For Single-Transition systems, where only one state may change in a transition rule, we show a bound of Î(log^{1/3} n), and for deterministic systems, where each pair of states may only have one associated transition rule, a bound of Î(({log n}/{log log n})^{1/2})
Game Characterization of Probabilistic Bisimilarity, and Applications to Pushdown Automata
We study the bisimilarity problem for probabilistic pushdown automata (pPDA)
and subclasses thereof. Our definition of pPDA allows both probabilistic and
non-deterministic branching, generalising the classical notion of pushdown
automata (without epsilon-transitions). We first show a general
characterization of probabilistic bisimilarity in terms of two-player games,
which naturally reduces checking bisimilarity of probabilistic labelled
transition systems to checking bisimilarity of standard (non-deterministic)
labelled transition systems. This reduction can be easily implemented in the
framework of pPDA, allowing to use known results for standard
(non-probabilistic) PDA and their subclasses. A direct use of the reduction
incurs an exponential increase of complexity, which does not matter in deriving
decidability of bisimilarity for pPDA due to the non-elementary complexity of
the problem. In the cases of probabilistic one-counter automata (pOCA), of
probabilistic visibly pushdown automata (pvPDA), and of probabilistic basic
process algebras (i.e., single-state pPDA) we show that an implicit use of the
reduction can avoid the complexity increase; we thus get PSPACE, EXPTIME, and
2-EXPTIME upper bounds, respectively, like for the respective non-probabilistic
versions. The bisimilarity problems for OCA and vPDA are known to have matching
lower bounds (thus being PSPACE-complete and EXPTIME-complete, respectively);
we show that these lower bounds also hold for fully probabilistic versions that
do not use non-determinism
Behavioural equivalences for timed systems
Timed transition systems are behavioural models that include an explicit
treatment of time flow and are used to formalise the semantics of several
foundational process calculi and automata. Despite their relevance, a general
mathematical characterisation of timed transition systems and their behavioural
theory is still missing. We introduce the first uniform framework for timed
behavioural models that encompasses known behavioural equivalences such as
timed bisimulations, timed language equivalences as well as their weak and
time-abstract counterparts. All these notions of equivalences are naturally
organised by their discriminating power in a spectrum. We prove that this
result does not depend on the type of the systems under scrutiny: it holds for
any generalisation of timed transition system. We instantiate our framework to
timed transition systems and their quantitative extensions such as timed
probabilistic systems
Non-Deterministic Kleene Coalgebras
In this paper, we present a systematic way of deriving (1) languages of
(generalised) regular expressions, and (2) sound and complete axiomatizations
thereof, for a wide variety of systems. This generalizes both the results of
Kleene (on regular languages and deterministic finite automata) and Milner (on
regular behaviours and finite labelled transition systems), and includes many
other systems such as Mealy and Moore machines
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