Results 1  10
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24
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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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 13 (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 7 (6 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.
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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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.
On the decidability of termination of query evaluation in transitiveclosure logics for polynomial constraint databases
, 2005
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A Decidable Class of Planar Linear Hybrid Systems
"... Abstract. The paper shows the decidability of the reachability problem for planar, monotonic, linear hybrid automata without resets. These automata are a special class of linear hybrid automata with only two variables, whose flows in all states is monotonic along some direction in the plane, and i ..."
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Abstract. The paper shows the decidability of the reachability problem for planar, monotonic, linear hybrid automata without resets. These automata are a special class of linear hybrid automata with only two variables, whose flows in all states is monotonic along some direction in the plane, and in which the continuous variables are not reset on a discrete transition. 1
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.
On the difficulty of deciding asymptotic stability of cubic homogeneous vector fields
 In Proceedings of the 2012 American Control Conference
, 2012
"... Abstract — It is wellknown that asymptotic stability (AS) of homogeneous polynomial vector fields of degree one (i.e., linear systems) can be decided in polynomial time e.g. by searching for a quadratic Lyapunov function. Since homogeneous vector fields of even degree can never be AS, the next inte ..."
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Abstract — It is wellknown that asymptotic stability (AS) of homogeneous polynomial vector fields of degree one (i.e., linear systems) can be decided in polynomial time e.g. by searching for a quadratic Lyapunov function. Since homogeneous vector fields of even degree can never be AS, the next interesting degree to consider is equal to three. In this paper, we prove that deciding AS of homogeneous cubic vector fields is strongly NPhard and pose the question of determining whether it is even decidable. As a byproduct of the reduction that establishes our NPhardness result, we obtain a Lyapunovinspired technique for proving positivity of forms. We also show that for asymptotically stable homogeneous cubic vector fields in as few as two variables, the minimum degree of a polynomial Lyapunov function can be arbitrarily large. Finally, we show that there is no monotonicity in the degree of polynomial Lyapunov functions that prove AS; i.e., a homogeneous cubic vector field with no homogeneous polynomial Lyapunov function of some degree d can very well have a homogeneous polynomial Lyapunov function of degree less than d. A. Background I.