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15
Termination of Linear Programs
 In CAV’2004: Computer Aided Verification, volume 3114 of LNCS
, 2004
"... We show that termination of a class of linear loop programs is decidable. Linear loop programs are discretetime linear systems with a loop condition governing termination, that is, a while loop with linear assignments. We relate the termination of such a simple loop, on all initial values, to t ..."
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Cited by 42 (0 self)
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We show that termination of a class of linear loop programs is decidable. Linear loop programs are discretetime linear systems with a loop condition governing termination, that is, a while loop with linear assignments. We relate the termination of such a simple loop, on all initial values, to the eigenvectors corresponding to only the positive real eigenvalues of the matrix defining the loop assignments. This characterization of termination is reminiscent of the famous stability theorems in control theory that characterize stability in terms of eigenvalues.
Termination of integer linear programs
 In Proc. CAV’06, LNCS 4144
, 2006
"... Abstract. We show that termination of a simple class of linear loops over the integers is decidable. Namely we show that termination of deterministic linear loops is decidable over the integers in the homogeneous case, and over the rationals in the general case. This is done by analyzing the powers ..."
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Cited by 12 (0 self)
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Abstract. We show that termination of a simple class of linear loops over the integers is decidable. Namely we show that termination of deterministic linear loops is decidable over the integers in the homogeneous case, and over the rationals in the general case. This is done by analyzing the powers of a matrix symbolically using its eigenvalues. Our results generalize the work of Tiwari [Tiw04], where similar results were derived for termination over the reals. We also gain some insights into termination of nonhomogeneous integer programs, that are very common in practice. 1
On Deciding Stability of Constrained Homogeneous Random Walks and Queueing Systems
 Mathematics of Operations Research
, 2000
"... We investigate stability of some scheduling policies in queueing systems. To the day no algorithmic characterization exists for checking stability of a given policy in a given queueing system. In this paper we propose a certain generalized priority policy and prove that the stability of this polic ..."
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Cited by 5 (4 self)
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We investigate stability of some scheduling policies in queueing systems. To the day no algorithmic characterization exists for checking stability of a given policy in a given queueing system. In this paper we propose a certain generalized priority policy and prove that the stability of this policy is algorithmically undecidable. We also prove that stability of a homogeneous random walk in Z d + is undecidable. To the best of our knowledge this is the first undecidability result in the area of stability of queueing systems and random walks in Z d + . We conjecture that stability of other common policies like FirstInFirstOut and priority policy is also an undecidable problem.
The discrete time behavior of lazy linear hybrid automata
 HSCC 2005. LNCS
, 2005
"... We study the class of lazy linear hybrid automata with finite precision. The key features of this class are: – The observation of the continuous state and the rate changes associated with mode switchings take place with bounded delays. – The values of the continuous variables can be observed with on ..."
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Cited by 5 (0 self)
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We study the class of lazy linear hybrid automata with finite precision. The key features of this class are: – The observation of the continuous state and the rate changes associated with mode switchings take place with bounded delays. – The values of the continuous variables can be observed with only finite precision. – The guards controlling the transitions of the automaton are finite conjunctions of arbitrary linear constraints. We show that the discrete time dynamics of this class of automata can be effectively analyzed without requiring resetting of the continuous variables during mode changes. In fact, our result holds for guard languages that go well beyond linear constraints.
Deciding termination of query evaluation in transitiveclosure logics for constraint databases
 In ICDT 2003
, 2003
"... The formalism of constraint databases, in which possibly infinite data sets are described by Boolean combinations of polynomial inequality and equality constraints, has its main application area in spatial databases. The standard query language for polynomial constraint databases is firstorder logi ..."
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Cited by 4 (2 self)
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The formalism of constraint databases, in which possibly infinite data sets are described by Boolean combinations of polynomial inequality and equality constraints, has its main application area in spatial databases. The standard query language for polynomial constraint databases is firstorder logic over the reals. Because of the limited expressive power of this logic with respect to queries that are important in spatial database applications, various extensions have been introduced. We study extensions of firstorder logic with different types of transitiveclosure operators and we are in particular interested in deciding the termination of the evaluation of queries expressible in these transitiveclosure logics. It turns out that termination is undecidable in general. However, we show that the termination of the transitive closure of a continuous function graph in the twodimensional plane, viewed as a binary relation over the reals, is decidable, and even expressible in firstorder logic over the reals. Based on this result, we identify a particular transitiveclosure logic for which termination of query evaluation is decidable and which is more expressive than firstorder logic over the reals. Furthermore, we can define a guarded fragment in which exactly the terminating queries of this language are expressible.
Analytical Tools for Natural Algorithms
 Proc. 1st ICS
, 2010
"... Abstract: We introduce an analytical tool to study the convergence of bidirectional multiagent agreement systems and use it to sharpen the analysis of various natural algorithms, including flocking, opinion consensus, and synchronization systems. We also improve classic bounds about colored random w ..."
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Cited by 4 (1 self)
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Abstract: We introduce an analytical tool to study the convergence of bidirectional multiagent agreement systems and use it to sharpen the analysis of various natural algorithms, including flocking, opinion consensus, and synchronization systems. We also improve classic bounds about colored random walks and discuss the usefulness of algorithmic proofs.
A On the Termination of Integer Loops
"... In this paper we study the decidability of termination of several variants of simple integer loops, without branching in the loop body and with affine constraints as the loop guard (and possibly a precondition). We show that termination of such loops is undecidable in some cases, in particular, when ..."
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Cited by 3 (0 self)
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In this paper we study the decidability of termination of several variants of simple integer loops, without branching in the loop body and with affine constraints as the loop guard (and possibly a precondition). We show that termination of such loops is undecidable in some cases, in particular, when the body of the loop is expressed by a set of linear inequalities where the coefficients are from Z∪{r} with r an arbitrary irrational; when the loop is a sequence of instructions, that compute either linear expressions or the step function; and when the loop body is a piecewise linear deterministic update with two pieces. The undecidability result is proven by a reduction from counter programs, whose termination is known to be undecidable. For the common case of integer linearconstraint loops with rational coefficients we have not succeeded in proving either decidability or undecidability of termination, but we show that a Petri net can be simulated with such a loop; this implies some interesting lower bounds. For example, termination for a partiallyspecified input is at least EXPSPACEhard.
Termination of Linear Programs
"... Abstract. We show that termination of a class of linear loop programs is decidable. Linear loop programs are discretetime linear systems with a loop condition governing termination, that is, a while loop with linear assignments. We relate the termination of such a simple loop, on all initial values ..."
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Abstract. We show that termination of a class of linear loop programs is decidable. Linear loop programs are discretetime linear systems with a loop condition governing termination, that is, a while loop with linear assignments. We relate the termination of such a simple loop, on all initial values, to the eigenvectors corresponding to only the positive real eigenvalues of the matrix defining the loop assignments. This characterization of termination is reminiscent of the famous stability theorems in control theory that characterize stability in terms of eigenvalues. 1 Introduction Dynamical systems have been studied by both computer scientists and controltheorists, but both the models and the properties studied have been different. However there is one class of models, called "discretetime linear systems " inthe control world, where there is a considerable overlap. In computer science, these are unconditional while loops with linear assignments to a set of integeror rational variables; for example, while (true) { x: = x y; y: = y}.The two communities are interested in different questions: stability and controllability issues in control theory against reachability, invariants, and terminationissues in computer science. In recent years, computer scientists have begun to apply the rich mathematical knowledge that has been developed in systems theoryfor analyzing such systems for safety properties, see for instance [17, 12, 11].
COMPUTATIONAL NEUROSCIENCE ORIGINAL RESEARCH ARTICLE
, 2012
"... Conductancebased neuron models and the slow dynamics of excitability ..."