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1
Content available remote SAT-Based Reachability Checking for Timed Automata with Discrete Data
100%
Zbrzezny A. , Półrola A.
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2007
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tom Vol. 79, nr 3-4
579-593
2
Content available remote On Almost-Sure Properties of Probabilistic Discrete Event Systems
80%
Yen H.-C.
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2011
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tom Vol. 110, nr 1-4
343-359
EN
Although randomization often increases the degree of flexibility in system design, analyzing system properties in the probabilistic framework introduces additional difficulties and challenges in comparison with their nonprobabilistic counterparts. In this paper, we focus on probabilistic versions of two problems frequently encountered in discrete event systems, namely, the reachability and forbidden-state problems. Our main concern is to see whether there exists a (or for every) non-blocking or fair control policy under which a given finite- or infinite-state system can be guided to reach (or avoid) a set of goal states with probability one. For finite-state systems, we devise algorithmic approaches which result in polynomial time solutions to the two problems. For infinite-state systems modelled as Petri nets, the problems are undecidable in general. For the class of persistent Petri nets, we establish a valuation approach through which the convergence behavior of a system is characterized, which in turn yields solutions to the reachability and forbidden-state problems.
3
Content available remote Reachability of cone fractional continuous-time linear systems
80%
Kaczorek T.
|
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nr 1
89-93
EN
A new class of cone fractional continuous-time linear systems is introduced. Necessary and sufficient conditions for a fractional linear system to be a cone fractional one are established. Sufficient conditions for the reachability of cone fractional systems are given. The discussion is illustrated with an example of linear cone fractional systems.
4
Content available remote Fractional positive continuous-time linear systems and their reachability
80%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
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2008
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tom 18
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nr 2
223-228
EN
A new class of fractional linear continuous-time linear systems described by state equations is introduced. The solution to the state equations is derived using the Laplace transform. Necessary and sufficient conditions are established for the internal and external positivity of fractional systems. Sufficient conditions are given for the reachability of fractional positive systems.
5
Content available Reachability of standard and fractional continuous-time systems with constant inputs
80%
Rogowski K.
Archives of Control Sciences
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2016
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tom Vol. 26, no. 2
147--159
EN
The reachability of standard and fractional-order continuous-time systems with constant inputs is addressed. Positive and non-positive continuous-time linear systems are considered. Necessary and sufficient conditions for the existence of such constant inputs that steers the system from zero initial conditions to the given final state in desired time are derived and proved. As an example of such systems the electrical circuits with DC voltage sources are presented
6
Content available remote Relating Reachability Problems in Timed and Counter Automata
80%
Haase C. , Ouaknine J. , Worrell J.
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tom Vol. 143, nr 3/4
317--338
EN
We establish a relationship between reachability problems in timed automata and spacebounded counter automata. We show that reachability in timed automata with three or more clocks is logarithmic-space inter-reducible with reachability in space-bounded counter automata with two counters. We moreover show the logarithmic-space equivalence of reachability in two-clock timed automata and space-bounded one-counter automata. This last reduction has recently been employed by Fearnley and Jurdziński to settle the computational complexity of reachability in two-clock timed automata.
7
Content available remote Positive 2D discrete-time linear Lyapunov systems
80%
Przyborowski P. , Kaczorek T.
|
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nr 1
95-105
EN
Two models of positive 2D discrete-time linear Lyapunov systems are introduced. For both the models necessary and sufficient conditions for positivity, asymptotic stability, reachability and observability are established. The discussion is illustrated with numerical examples.
8
Content available remote Computation of fundamental matrices and reachability of positive singular discrete linear systems
80%
Kaczorek T.
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1998
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tom Vol. 46, nr 4
501-511
EN
Positive singular discrete linear time-invariant systems are considered. Some properties of the fundamental matrix and solutions of the positive singular discrete linear systems are characterised. Two new methods for computation of the fundamental matrices are proposed. Necessary and sufficient conditions are established for the reachability of the positive singular systems. Sufficient conditions are given for unreachability of the systems.
9
Content available remote Reachability, controllability to zero and observability of the positive discrete-time Lyapunov systems
80%
Kaczorek T. , Przyborowski P.
Control and Cybernetics
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2009
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tom Vol. 38, no 2
529-541
EN
The new necessary and sufficient conditions for the reachability, controllability to zero and observability of the positive discrete-time Lyapunov systems are established. The notion of the dual positive Lyapunov system is introduced and the relationship between the reachability and observability are given. The considerations are illustrated with numerical examples.
10
Content available remote The Reachability Problem for Object Nets
80%
Köhler M.
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2007
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tom Vol. 79, nr 3-4
401-413
EN
In this article I will prove undecidability results for elementary object net systems ( EOS). Object nets are Petri nets which have Petri nets as tokens - an approach which is called the "nets-within-nets" paradigm. EOS are special object net systems which have a two leveled structure.
11
Content available Minimum energy control of positive 2D continuous-discrete linear systems with bounded inputs
70%
Kaczorek T.
Archives of Control Sciences
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2015
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tom Vol. 25, no. 3
319--331
EN
A new formulation of the minimum energy control problem for the positive 2D continuousdiscrete linear systems with bounded inputs is proposed. Necessary and sufficient conditions for the reachability of the systems are established. Conditions for the existence of the solution to the minimum energy control problem and a procedure for computation of an input minimizing the given performance index are given. Effectiveness of the procedure is demonstrated on numerical example.
12
Content available remote Using logic programs with stable model semantics to solve deadlock and reachability problems for 1-safe Petri Nets
70%
Heljanko K.
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1999
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tom Vol. 37, Nr 3
247-268
EN
McMillan has presented a deadlock detection method for Petri nets based on finite complete prefixes (i.e. net unfoldings). The approach transforms the PSPACE-complete deadlock detec-tion problem for a 1-safe Petri net into a potentially exponentially larger NP-complete prob-lem of deadlock detection for a finite complete prefix. McMillan devised a branch-and-bound algorithm for deadlock detection in prefixes. Recently, Melzer and Römer have presented another approach, which is based on solving mixed integer programming problems. In this work it is shown that instead of using mixed integer programming, a constraint-based logic programming framework can be employed, and a linear-size, translation from deadlock detec-tion in prefixes into the problem of finding a stable model of a logic program is presented. As a side result also such a translation for solving the reachability problem is devised. Correct-ness proofs of both the translations are presented. Experimental results are given from an im-plementation combining the prefix generator of the PEP-tool, the translation, and an imple-mentation of a constraint-based logic programming framework, the smodels system. The ex-periments show the proposed approach to be quite competitive, when compared to the ap-proaches of McMillan and Melzer/Römer.
13
Content available remote Reachability and controllability to zero of cone fractional linear systems
70%
Kaczorek T.
Archives of Control Sciences
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2007
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tom Vol. 17, no. 4
357-367
EN
A new class of cone fractional linear discrete-time systems is introduced. Necessary and sufficient conditions for the reachability and controllability to zero of the cone fractional systems are established.
14
Content available remote A Survey of Decidability Results for Elementary Object Systems
70%
Köhler-Bußmeier M.
Fundamenta Informaticae
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2014
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tom Vol. 130, nr 1
99--123
EN
This contribution presents recent results on Elementary Object Systems (EOS). Object nets are Petri nets which have Petri nets as tokens – an approach known as the nets-within-nets paradigm. In this work we study the relationship of EOS to existing Petri net formalisms. It turns out that EOS are equivalent to counter programs. But even for the restricted subclass of conservative EOS reachability and liveness are undecidable problems. On the other hand for other properties like boundedness are still decidable for conservative EOS. We also study the sub-class of generalised state machines, which is worth mentioning since it combines decidability of many theoretically interesting properties with a quite rich practical modelling expressiveness.
15
Content available Invariant properties of positive linear electrical circuits
70%
Kaczorek T.
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tom Vol. 68, nr 4
875--890
EN
The invariant properties of the stability, reachability, observability and transfer matrices of positive linear electrical circuits with integer and fractional orders are investigated. It is shown that the stability, reachability, observability and transfer matrix of positive linear systems are invariant under their integer and fractional orders.
16
Content available remote Reachability Analysis for Timed Automata Based on Partitioning
70%
Półrola A. , Penczek W. , Szreter M.
Prace Instytutu Podstaw Informatyki Polskiej Akademii Nauk
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2003
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tom Nr 961
1-23
EN
Model checking is an approach commonly applied for automated verification of reachability properties. Given a system $S$ and a property $p$, reachability model checking consists in an exploration of the state space of $S$, checking whether there exists a state where $p$ holds. Since concrete state spaces (models) of timed systems are usually infinite, they cannot be directly applied to model checking. One of the solution to this problem is to exploit finite abstract models, preseving the properties of interest. The paper presents a new method of buildng abstract models for Timed Automata, based on a partitioning algorithm. Our pseudo-bisimulating models are often smaller than forward-reachability graphs , commonly used in reachability analysis. The method enables verification on-the-fly, i.e., generating of the model can be stopped as soon as a state satisfying $p$ is found.
PL
Automatyczne testowanie osiągalności wykonywane jest zazwyczaj za pomocą metod weryfikacji modelowej. Dla danego systemy S i właściwości p polega ono na przejrzeniu przestrzeni stanów S i sprawdzeniu, czy zawiera ona stan w którym p zachodzi. Istotne znaczenie ma zatem rozmiar przeglądanej przestrzeni (modelu), który w wielu przypadkach (np. dla systemów z czasem) może być nawet nieskończony. Jednym z możliwych rozwiązań jest zastosowanie skończonych modeli abstrakcyjnych zachowujących żądane własności. Praca przedstawia nową metodę generowania modeli abstrakcyjnych dla automatów czasowych, bazujących na algorytmie minimalizacji (podziału). Otrzymywane modele pseudobisymulacyjne zachowują osiągalność, a przy tym są często mniejsze niż używane zwykle do jej testowania tzw. grafy forward-reachability. Metoda pozawala też na wykonywanie weryfikacji "w locie", tj. przerywanie budowania modelu gdy wygenerowany zostanie stan spełniający p.
17
Content available remote Monomial subdigraphs of reachable and controllable positive discrete-time systems
70%
Bru R. , Caccetta L. , Rumchev V. G.
International Journal of Applied Mathematics and Computer Science
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2005
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tom 15
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nr 1
159-166
EN
A generic structure of reachable and controllable positive linear systems is given in terms of some characteristic components (monomial subdigraphs) of the digraph of a non-negative a pair. The properties of monomial subdigraphs are examined and used to derive reachability and controllability criteria in a digraph form for the general case when the system matrix may contain zero columns. The graph-theoretic nature of these criteria makes them computationally more efficient than their known equivalents. The criteria identify not only the reachability and controllability properties of positive linear systems, but also their reachable and controllable parts (subsystems) when the system does not possess such properties.
18
Content available remote Reachability and Controllability of Positive Continuous Time Linear Systems with Time Variable Coefficients
70%
Klamka J. , Kalinowski J.
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2001
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tom vol. 49, nr 4
633-641
EN
In the paper using pure algebraic methods new sufficient conditions for reachability and controllability of positive linear continuous-time finite-dimensional dynamical systems with variable coefficients are established. As a special case linear dynamical systems with constant coefficients are also considered. Illustrative example is also given.
19
Content available remote Analysis of some dual properties in discrete dynamic systems
70%
Zhirabok A.
International Journal of Applied Mathematics and Computer Science
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2006
|
tom 16
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nr 3
297-308
EN
The problem of duality in nonlinear and linear systems is considered. In addition to the known duality between controllability and observability, new dual notions and their properties are investigated. A way to refine these properties through an isomorphic transformation of the original systems is suggested.
20
Content available remote An Upper Bound for the Reachability Problem of Safe, Elementary Hornets
70%
Köhler-Bußmeier M. , Heitmann F.
Fundamenta Informaticae
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2016
|
tom Vol. 143, nr 1/2
89--100
EN
In this paper we study the complexity of the reachability problem HORNETS, an algebraic extension of object nets. Here we consider the restricted class of safe, elementary HORNETS. In previouswork we established the lower bound, i.e. reachability requires at least exponential space. In another work we have shown we can simulate elementary HORNETS with elementary object nets EOS, where reachability is known to be PSpace-complete. Since this simulation leads to a double exponential increase in the size of the simulating EOS, we obtain that for HORNETS the reachability problem is solvable in double exponential space. In this contributionwe show that this kind of simulation is rather bad, since we show that exponential space is sufficient. Together with the known lower bound this shows that the upper is tight.
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