234,926 research outputs found
Soundness in Negotiations
Negotiations are a formalism for describing multiparty distributed cooperation. Alternatively, they can be seen as a model of concurrency with synchronized choice as communication primitive. Well-designed negotiations must be sound, meaning that, whatever its current state, the negotiation can still be completed. In a former paper, Esparza and Desel have shown that deciding soundness of a negotiation is PSPACE-complete, and in PTIME if the negotiation is deterministic. They have also provided an algorithm for an intermediate class of acyclic, non-deterministic negotiations, but left the complexity of the soundness problem open.
In the first part of this paper we study two further analysis problems for sound acyclic deterministic negotiations, called the race and the omission problem, and give polynomial algorithms. We use these results to provide the first polynomial algorithm for some analysis problems of workflow nets with data previously studied by Trcka, van der Aalst, and Sidorova.
In the second part we solve the open question of Esparza and Desel\u27s paper. We show that soundness of acyclic, weakly non-deterministic negotiations is in PTIME, and that checking soundness is already NP-complete for slightly more general classes
Achieving New Upper Bounds for the Hypergraph Duality Problem through Logic
The hypergraph duality problem DUAL is defined as follows: given two simple
hypergraphs and , decide whether
consists precisely of all minimal transversals of (in which case
we say that is the dual of ). This problem is
equivalent to deciding whether two given non-redundant monotone DNFs are dual.
It is known that non-DUAL, the complementary problem to DUAL, is in
, where
denotes the complexity class of all problems that after a nondeterministic
guess of bits can be decided (checked) within complexity class
. It was conjectured that non-DUAL is in . In this paper we prove this conjecture and actually
place the non-DUAL problem into the complexity class which is a subclass of . We here refer to the logtime-uniform version of
, which corresponds to , i.e., first order
logic augmented by counting quantifiers. We achieve the latter bound in two
steps. First, based on existing problem decomposition methods, we develop a new
nondeterministic algorithm for non-DUAL that requires to guess
bits. We then proceed by a logical analysis of this algorithm, allowing us to
formulate its deterministic part in . From this result, by
the well known inclusion , it follows
that DUAL belongs also to . Finally, by exploiting
the principles on which the proposed nondeterministic algorithm is based, we
devise a deterministic algorithm that, given two hypergraphs and
, computes in quadratic logspace a transversal of
missing in .Comment: Restructured the presentation in order to be the extended version of
a paper that will shortly appear in SIAM Journal on Computin
Deterministic regression model and visual basic code for optimal.
A new, non-statistical method is presented for analysis of the past history and current evolution of economic and financial processes. The method is based on the sliding model approach using linear differential or difference equations applied to discrete information in the form of known chronological data (time series) about the process. An algorithm is proposed that allows one to project the current evolution of the process onto some period of its future development. Computer code in visual basic is developed that has been validated in application to American stock index S&P 500, with predicted values within 5% of real data over long periods of the recent past history. The algorithm and the code can be applied to practical problems in finance and economy in time of its normal evolution without catastrophic events.Sliding deterministic regression models; Optimal forecasting in finance;
Spectral analysis of the Gram matrix of mixture models
This text is devoted to the asymptotic study of some spectral properties of
the Gram matrix built upon a collection of random vectors (the columns of ), as both the number of
observations and the dimension of the observations tend to infinity and are
of similar order of magnitude. The random vectors are
independent observations, each of them belonging to one of classes
. The observations of each class
() are characterized by their distribution
, where are some non negative
definite matrices. The cardinality of class
and the dimension of the observations are such that () and stay bounded away from and . We provide
deterministic equivalents to the empirical spectral distribution of and to the matrix entries of its resolvent (as well as of the resolvent of
). These deterministic equivalents are defined thanks to the
solutions of a fixed-point system. Besides, we prove that has
asymptotically no eigenvalues outside the bulk of its spectrum, defined thanks
to these deterministic equivalents. These results are directly used in our
companion paper "Kernel spectral clustering of large dimensional data", which
is devoted to the analysis of the spectral clustering algorithm in large
dimensions. They also find applications in various other fields such as
wireless communications where functionals of the aforementioned resolvents
allow one to assess the communication performance across multi-user
multi-antenna channels.Comment: 25 pages, 1 figure. The results of this paper are directly used in
our companion paper "Kernel spectral clustering of large dimensional data",
which is devoted to the analysis of the spectral clustering algorithm in
large dimensions. To appear in ESAIM Probab. Statis
Attribute Exploration of Discrete Temporal Transitions
Discrete temporal transitions occur in a variety of domains, but this work is
mainly motivated by applications in molecular biology: explaining and analyzing
observed transcriptome and proteome time series by literature and database
knowledge. The starting point of a formal concept analysis model is presented.
The objects of a formal context are states of the interesting entities, and the
attributes are the variable properties defining the current state (e.g.
observed presence or absence of proteins). Temporal transitions assign a
relation to the objects, defined by deterministic or non-deterministic
transition rules between sets of pre- and postconditions. This relation can be
generalized to its transitive closure, i.e. states are related if one results
from the other by a transition sequence of arbitrary length. The focus of the
work is the adaptation of the attribute exploration algorithm to such a
relational context, so that questions concerning temporal dependencies can be
asked during the exploration process and be answered from the computed stem
base. Results are given for the abstract example of a game and a small gene
regulatory network relevant to a biomedical question.Comment: Only the email address and reference have been replace
A -Competitive Algorithm for Scheduling Packets with Deadlines
In the online packet scheduling problem with deadlines (PacketScheduling, for
short), the goal is to schedule transmissions of packets that arrive over time
in a network switch and need to be sent across a link. Each packet has a
deadline, representing its urgency, and a non-negative weight, that represents
its priority. Only one packet can be transmitted in any time slot, so, if the
system is overloaded, some packets will inevitably miss their deadlines and be
dropped. In this scenario, the natural objective is to compute a transmission
schedule that maximizes the total weight of packets which are successfully
transmitted. The problem is inherently online, with the scheduling decisions
made without the knowledge of future packet arrivals. The central problem
concerning PacketScheduling, that has been a subject of intensive study since
2001, is to determine the optimal competitive ratio of online algorithms,
namely the worst-case ratio between the optimum total weight of a schedule
(computed by an offline algorithm) and the weight of a schedule computed by a
(deterministic) online algorithm.
We solve this open problem by presenting a -competitive online
algorithm for PacketScheduling (where is the golden ratio),
matching the previously established lower bound.Comment: Major revision of the analysis and some other parts of the paper.
Another revision will follo
Alternative Automata-based Approaches to Probabilistic Model Checking
In this thesis we focus on new methods for probabilistic model checking (PMC) with linear temporal logic (LTL). The standard approach translates an LTL formula into a deterministic Ï-automaton with a double-exponential blow up.
There are approaches for Markov chain analysis against LTL with exponential runtime, which motivates the search for non-deterministic automata with restricted forms of non-determinism that make them suitable for PMC. For MDPs, the approach via deterministic automata matches the double-exponential lower bound, but a practical application might benefit from approaches via non-deterministic automata.
We first investigate good-for-games (GFG) automata. In GFG automata one can resolve the non-determinism for a finite prefix without knowing the infinite suffix and still obtain an accepting run for an accepted word. We explain that GFG automata are well-suited for MDP analysis on a theoretic level, but our experiments show that GFG automata cannot compete with deterministic automata.
We have also researched another form of pseudo-determinism, namely unambiguity, where for every accepted word there is exactly one accepting run. We present a polynomial-time approach for PMC of Markov chains against specifications given by an unambiguous BĂŒchi automaton (UBA). Its two key elements are the identification whether the induced probability is positive, and if so, the identification of a state set inducing probability 1.
Additionally, we examine the new symbolic Muller acceptance described in the Hanoi Omega Automata Format, which we call Emerson-Lei acceptance. It is a positive Boolean formula over unconditional fairness constraints. We present a construction of small deterministic automata using Emerson-Lei acceptance. Deciding, whether an MDP has a positive maximal probability to satisfy an Emerson-Lei acceptance, is NP-complete. This fact has triggered a DPLL-based algorithm for deciding positiveness
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