22,852 research outputs found
Synchronous and Asynchronous Recursive Random Scale-Free Nets
We investigate the differences between scale-free recursive nets constructed
by a synchronous, deterministic updating rule (e.g., Apollonian nets), versus
an asynchronous, random sequential updating rule (e.g., random Apollonian
nets). We show that the dramatic discrepancies observed recently for the degree
exponent in these two cases result from a biased choice of the units to be
updated sequentially in the asynchronous version
Wadge Degrees of -Languages of Petri Nets
We prove that -languages of (non-deterministic) Petri nets and
-languages of (non-deterministic) Turing machines have the same
topological complexity: the Borel and Wadge hierarchies of the class of
-languages of (non-deterministic) Petri nets are equal to the Borel and
Wadge hierarchies of the class of -languages of (non-deterministic)
Turing machines which also form the class of effective analytic sets. In
particular, for each non-null recursive ordinal there exist some -complete and some -complete -languages of Petri nets, and the supremum of
the set of Borel ranks of -languages of Petri nets is the ordinal
, which is strictly greater than the first non-recursive ordinal
. We also prove that there are some -complete, hence non-Borel, -languages of Petri nets, and
that it is consistent with ZFC that there exist some -languages of
Petri nets which are neither Borel nor -complete. This
answers the question of the topological complexity of -languages of
(non-deterministic) Petri nets which was left open in [DFR14,FS14].Comment: arXiv admin note: text overlap with arXiv:0712.1359, arXiv:0804.326
Decidable Models of Recursive Asynchronous Concurrency
Asynchronously communicating pushdown systems (ACPS) that satisfy the
empty-stack constraint (a pushdown process may receive only when its stack is
empty) are a popular decidable model for recursive programs with asynchronous
atomic procedure calls. We study a relaxation of the empty-stack constraint for
ACPS that permits concurrency and communication actions at any stack height,
called the shaped stack constraint, thus enabling a larger class of concurrent
programs to be modelled. We establish a close connection between ACPS with
shaped stacks and a novel extension of Petri nets: Nets with Nested Coloured
Tokens (NNCTs). Tokens in NNCTs are of two types: simple and complex. Complex
tokens carry an arbitrary number of coloured tokens. The rules of NNCT can
synchronise complex and simple tokens, inject coloured tokens into a complex
token, and eject all tokens of a specified set of colours to predefined places.
We show that the coverability problem for NNCTs is Tower-complete. To our
knowledge, NNCT is the first extension of Petri nets, in the class of nets with
an infinite set of token types, that has primitive recursive coverability. This
result implies Tower-completeness of coverability for ACPS with shaped stacks
Fractal and Transfractal Recursive Scale-Free Nets
We explore the concepts of self-similarity, dimensionality, and
(multi)scaling in a new family of recursive scale-free nets that yield
themselves to exact analysis through renormalization techniques. All nets in
this family are self-similar and some are fractals - possessing a finite
fractal dimension - while others are small world (their diameter grows
logarithmically with their size) and are infinite-dimensional. We show how a
useful measure of "transfinite" dimension may be defined and applied to the
small world nets. Concerning multiscaling, we show how first-passage time for
diffusion and resistance between hub (the most connected nodes) scale
differently than for other nodes. Despite the different scalings, the Einstein
relation between diffusion and conductivity holds separately for hubs and
nodes. The transfinite exponents of small world nets obey Einstein relations
analogous to those in fractal nets.Comment: Includes small revisions and references added as result of readers'
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Finite petri nets as models for recursive causal behaviour
Goltz (1988) discussed whether or not there exist finite Petri nets (with unbounded capacities) modelling the causal behaviour of certain recursive CCS terms. As a representative example, the following term is considered: \ud
\ud
B=(a.nilb.B)+c.nil. \ud
\ud
We will show that the answer depends on the chosen notion of behaviour. It was already known that the interleaving behaviour and the branching structure of terms as B can be modelled as long as causality is not taken into account. We now show that also the causal behaviour of B can be modelled as long as the branching structure is not taken into account. However, it is not possible to represent both causal dependencies and the behaviour with respect to choices between alternatives in a finite net. We prove that there exists no finite Petri net modelling B with respect to both pomset trace equivalence and failure equivalence
Safe Recursion on Notation into a Light Logic by Levels
We embed Safe Recursion on Notation (SRN) into Light Affine Logic by Levels
(LALL), derived from the logic L4. LALL is an intuitionistic deductive system,
with a polynomial time cut elimination strategy.
The embedding allows to represent every term t of SRN as a family of proof
nets |t|^l in LALL. Every proof net |t|^l in the family simulates t on
arguments whose bit length is bounded by the integer l. The embedding is based
on two crucial features. One is the recursive type in LALL that encodes Scott
binary numerals, i.e. Scott words, as proof nets. Scott words represent the
arguments of t in place of the more standard Church binary numerals. Also, the
embedding exploits the "fuzzy" borders of paragraph boxes that LALL inherits
from L4 to "freely" duplicate the arguments, especially the safe ones, of t.
Finally, the type of |t|^l depends on the number of composition and recursion
schemes used to define t, namely the structural complexity of t. Moreover, the
size of |t|^l is a polynomial in l, whose degree depends on the structural
complexity of t.
So, this work makes closer both the predicative recursive theoretic
principles SRN relies on, and the proof theoretic one, called /stratification/,
at the base of Light Linear Logic
Couverture et Terminaison dans les réseaux de Petri Récursifs
International audienceIn the early two-thousands, Recursive Petri nets have been introduced in order to model distributed planning of multi-agent systems for which counters and recursivity were necessary. Although Recursive Petri nets strictly extend Petri nets and stack automata, most of the usual property problems are solvable but using non primitive recursive algorithms, even for coverability and termination. For almost all other extended Petri nets models containing a stack the complexity of coverability and termination are unknown or strictly larger than EXPSPACE. In contrast, we establish here that for Recursive Petri nets, the coverability and termination problems are EXPSPACE-complete as for Petri nets. From an expressiveness point of view, we show that coverability languages of Recursive Petri nets strictly include the union of coverability languages of Petri nets and context-free languages. Thus we get for free a more powerful model than Petri net
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