97,168 research outputs found
On the Size of Finite Rational Matrix Semigroups
Let be a positive integer and a set of rational -matrices such that generates a finite multiplicative semigroup.
We show that any matrix in the semigroup is a product of matrices in whose length is at most ,
where is the maximum order of finite groups over rational -matrices. This result implies algorithms with an elementary running time for
deciding finiteness of weighted automata over the rationals and for deciding
reachability in affine integer vector addition systems with states with the
finite monoid property
An Approach to Regular Separability in Vector Addition Systems
We study the problem of regular separability of languages of vector addition
systems with states (VASS). It asks whether for two given VASS languages K and
L, there exists a regular language R that includes K and is disjoint from L.
While decidability of the problem in full generality remains an open question,
there are several subclasses for which decidability has been shown: It is
decidable for (i) one-dimensional VASS, (ii) VASS coverability languages, (iii)
languages of integer VASS, and (iv) commutative VASS languages. We propose a
general approach to deciding regular separability. We use it to decide regular
separability of an arbitrary VASS language from any language in the classes
(i), (ii), and (iii). This generalizes all previous results, including (iv)
Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS
Vector Addition Systems with States (VASS) provide a well-known and
fundamental model for the analysis of concurrent processes, parameterized
systems, and are also used as abstract models of programs in resource bound
analysis. In this paper we study the problem of obtaining asymptotic bounds on
the termination time of a given VASS. In particular, we focus on the
practically important case of obtaining polynomial bounds on termination time.
Our main contributions are as follows: First, we present a polynomial-time
algorithm for deciding whether a given VASS has a linear asymptotic complexity.
We also show that if the complexity of a VASS is not linear, it is at least
quadratic. Second, we classify VASS according to quantitative properties of
their cycles. We show that certain singularities in these properties are the
key reason for non-polynomial asymptotic complexity of VASS. In absence of
singularities, we show that the asymptotic complexity is always polynomial and
of the form , for some integer , where is the
dimension of the VASS. We present a polynomial-time algorithm computing the
optimal . For general VASS, the same algorithm, which is based on a complete
technique for the construction of ranking functions in VASS, produces a valid
lower bound, i.e., a such that the termination complexity is .
Our results are based on new insights into the geometry of VASS dynamics, which
hold the potential for further applicability to VASS analysis.Comment: arXiv admin note: text overlap with arXiv:1708.0925
The Hardness of Finding Linear Ranking Functions for Lasso Programs
Finding whether a linear-constraint loop has a linear ranking function is an
important key to understanding the loop behavior, proving its termination and
establishing iteration bounds. If no preconditions are provided, the decision
problem is known to be in coNP when variables range over the integers and in
PTIME for the rational numbers, or real numbers. Here we show that deciding
whether a linear-constraint loop with a precondition, specifically with
partially-specified input, has a linear ranking function is EXPSPACE-hard over
the integers, and PSPACE-hard over the rationals. The precise complexity of
these decision problems is yet unknown. The EXPSPACE lower bound is derived
from the reachability problem for Petri nets (equivalently, Vector Addition
Systems), and possibly indicates an even stronger lower bound (subject to open
problems in VAS theory). The lower bound for the rationals follows from a novel
simulation of Boolean programs. Lower bounds are also given for the problem of
deciding if a linear ranking-function supported by a particular form of
inductive invariant exists. For loops over integers, the problem is PSPACE-hard
for convex polyhedral invariants and EXPSPACE-hard for downward-closed sets of
natural numbers as invariants.Comment: In Proceedings GandALF 2014, arXiv:1408.5560. I thank the organizers
of the Dagstuhl Seminar 14141, "Reachability Problems for Infinite-State
Systems", for the opportunity to present an early draft of this wor
New space vector modulation algorithms applied to multilevel converters with balanced DC-link voltage
This work presents a survey of new space vector modulation algorithms for high power voltage source multilevel converters. These techniques provide the nearest switching vectors sequence to the reference vector and calculates the on-state durations of the respective switching state vectors without involving trigonometric functions, look-up tables or coordinate system transformations which increase the computational load corresponding to the modulation of a multilevel converter. These algorithms drastically reduce the computational load maintained permitting the on-line computation of the switching sequence and the on-state durations of the respective switching state vectors. The on-state durations are reduced to a simple addition. In addition, the low computational cost of the proposed methods is always the same and it is independent of the number of levels of the converter. The algorithms have been satisfactorily implemented in very low-cost microcontrollers.Ministerio de Ciencia y Tecnología DPI 2001-308
- …