scholarly journals Local Computation of Simultaneous Fixed-Points

2003 ◽  
Vol 21 (420) ◽  
Author(s):  
Henrik Reif Andersen
Keyword(s):  
Model Checking ◽  
Fixed Points ◽  
Ad Hoc ◽  
General Algorithm ◽  
General Mechanism ◽  
Local Algorithm ◽  
Worst Case ◽  
Local Algorithms ◽  
Logarithmic Factor ◽  
Strictness Analysis

<!--DAIMI Standard Header Begin--> <p>We present a very simple, yet general algorithm for computing simultaneous, minimum fixed-points of monotonic functions, or turning the newpoint slightly, an algorithm for computing minimum solutions to a system of monotonic equations. The algorithm is local (demand-driven, lazy, ... ), i.e. it will try to determine the value of a single component in the simultaneous fixed-point by investigating only certain necessary parts of the description of the monotonic function, or in terms of the equational presentation, it will determine the value of a single variable by investigating only a part of the equational system.</p><p>In the worst-case this involves inspecting the complete system, and the algorithm will be a logarithmic factor worse than a global algorithm (computing the values of all variables simultaneously). But despite its simplicity the local algorithm has some advantages which promise much better performance on typical cases. The algorithm should be seen as a schema that for any particular application needs to be refined to achieve better efficiency, but the general mechanism remains the same. As such it seems to achieve performance comparable to, and for some examples improving upon, carefully designed <em>ad hoc</em> algorithms, still maintaining the benefits of being local.</p><p>We illustrate this point by tailoring the general algorithm to concrete examples in such (apparently) diverse areas as type inference, model checking, and strictness analysis. Especially in connection with the last example, strictness analysis, and more generally abstract interpretation, it is illustrated how the local algorithm provides a very minimal approach when determining the fixed-points, reminiscent of, but improving upon, what is known as Pending Analysis. In the case of model checking a specialised version of the algorithm has already improved on earlier known local algorithms.</p>

Fixed Points- Noncontractive Functions

2001 ◽  
Author(s):  
Krzysztof A. Sikorski
Keyword(s):  
Fixed Points ◽  
Absolute Error ◽  
Small Error ◽  
Homotopy Continuation ◽  
Average Case Analysis ◽  
Error Criterion ◽  
Worst Case ◽  
Average Case ◽  
Worst Case Complexity ◽  
Exponential Complexity

In this chapter we consider the approximation of fixed points of noncontractive functions with respect to the absolute error criterion. In this case the functions may have multiple and/or whole manifolds of fixed points. We analyze methods based on sequential function evaluations as information. The simple iteration usually does not converge in this case, and the problem becomes much more difficult to solve. We prove that even in the two-dimensional case the problem has infinite worst case complexity. This means that no methods exist that solve the problem with arbitrarily small error tolerance for some “bad” functions. In the univariate case the problem is solvable, and a bisection envelope method is optimal. These results are in contrast with the solution under the residual error criterion. The problem then becomes solvable, although with exponential complexity, as outlined in the annotations. Therefore, simplicial and/or homotopy continuation and all methods based on function evaluations exhibit exponential worst case cost for solving the problem in the residual sense. These results indicate the need of average case analysis, since for many test functions the existing algorithms computed ε-approximations with polynomial in 1/ε cost.

Reliability-Aware Proactive Energy Management in Hard Real-Time Systems

2010 ◽  
Vol 1 (4) ◽  
pp. 1-11
Author(s):  
Satyakiran Munaga ◽  
Francky Catthoor
Keyword(s):  
Energy Management ◽  
Ad Hoc ◽  
Failure Criteria ◽  
Worst Case ◽  
Time Control ◽  
Run Time ◽  
Cost Penalty ◽  
Hard Real Time ◽  
The Cost ◽  
Time Systems

Advanced technologies such as sub-45nm CMOS and 3D integration are known to have more accelerated and increased number of reliability failure mechanisms. Classical reliability assessment methodology, which assumes ad-hoc failure criteria and worst-case for all influencing dynamic aspects, is no longer viable in these technologies. In this paper, the authors advocate that managing temperature and reliability at run-time is necessary to overcome this reliability-wall without incurring significant cost penalty. Nonlinear nature of modern systems, however, makes the run-time control very challenging. The authors suggest that full cost-consciousness requires a truly proactive controller that can efficiently manage system slack with future in perspective. This paper introduces the concept of “gas-pedal,” which enhances the effectiveness of the proactive controller in minimizing the cost without sacrificing the hard guarantees required by the constraints. Reliability-aware dynamic energy management of a processor running AVC motion compensation task is used as a motivational case study to illustrate the proposed concepts.

Local Algorithms for Topology Control in Ad-Hoc Networks

2010 ◽  
pp. 51-58
Author(s):  
Evangelos Kranakis ◽  
Jorge Urrutia
Keyword(s):  
Topology Control ◽  
Ad Hoc ◽  
Edge Coloring ◽  
Dominating Sets ◽  
Open Problems ◽  
Local Algorithms ◽  
Trade Offs ◽  
The Subject ◽  
Hoc Networks ◽  
Local Topology

In this chapter, we present a survey of recent techniques for local topology control in location aware Unit Disk Graphs including local algorithms for Routing, Traversal, Planar Spanners, Dominating and Connected Dominating Sets, and Vertex and Edge Coloring. In addition to investigating trade-offs for these problems, we discuss open problems that will play an important role in the future development of the subject.

A Methodology for Model-Checking Ad-hoc Networks

2003 ◽  
pp. 181-196 ◽  
Author(s):  
Irfan Zakiuddin ◽  
Michael Goldsmith ◽  
Paul Whittaker ◽  
Paul Gardiner
Keyword(s):  
Model Checking ◽  
Ad Hoc Networks ◽  
Ad Hoc ◽  
Hoc Networks

scholarly journals Logic-based specification and verification of homogeneous dynamic multi-agent systems

2020 ◽  
Vol 34 (2) ◽  
Author(s):  
Riccardo De Masellis ◽  
Valentin Goranko
Keyword(s):  
Normal Form ◽  
Model Checking ◽  
Formal Specification ◽  
Formal Semantics ◽  
Fixed Number ◽  
State Transitions ◽  
Multi Agent Systems ◽  
Worst Case ◽  
Worst Case Complexity ◽  
Multi Agent

Abstract We develop a logic-based framework for formal specification and algorithmic verification of homogeneous and dynamic concurrent multi-agent transition systems. Homogeneity means that all agents have the same available actions at any given state and the actions have the same effects regardless of which agents perform them. The state transitions are therefore determined only by the vector of numbers of agents performing each action and are specified symbolically, by means of conditions on these numbers definable in Presburger arithmetic. The agents are divided into controllable (by the system supervisor/controller) and uncontrollable, representing the environment or adversary. Dynamicity means that the numbers of controllable and uncontrollable agents may vary throughout the system evolution, possibly at every transition. As a language for formal specification we use a suitably extended version of Alternating-time Temporal Logic, where one can specify properties of the type “a coalition of (at least) n controllable agents can ensure against (at most) m uncontrollable agents that any possible evolution of the system satisfies a given objective $$\gamma$$ γ ″, where $$\gamma$$ γ is specified again as a formula of that language and each of n and m is either a fixed number or a variable that can be quantified over. We provide formal semantics to our logic $${\mathcal {L}}_{\textsc {hdmas}}$$ L H D M A S and define normal form of its formulae. We then prove that every formula in $${\mathcal {L}}_{\textsc {hdmas}}$$ L H D M A S is equivalent in the finite to one in a normal form and develop an algorithm for global model checking of formulae in normal form in finite HDMAS models, which invokes model checking truth of Presburger formulae. We establish worst case complexity estimates for the model checking algorithm and illustrate it on a running example.

Model checking mobile ad hoc networks

2016 ◽  
Vol 49 (3) ◽  
pp. 159-189 ◽  
Author(s):  
Fatemeh Ghassemi ◽  
Wan Fokkink
Keyword(s):  
Model Checking ◽  
Ad Hoc Networks ◽  
Mobile Ad Hoc Networks ◽  
Ad Hoc ◽  
Mobile Ad Hoc ◽  
Hoc Networks

TWO LOCAL STRATEGY ITERATION SCHEMES FOR PARITY GAME SOLVING

2012 ◽  
Vol 23 (03) ◽  
pp. 669-685 ◽  
Author(s):  
OLIVER FRIEDMANN ◽  
MARTIN LANGE
Keyword(s):  
Model Checking ◽  
Winning Strategy ◽  
Fractional Part ◽  
Program Synthesis ◽  
Global Strategy ◽  
Local Algorithm ◽  
The Core ◽  
Local Strategy ◽  
Parity Games ◽  
Satisfiability Checking

The problem of solving a parity game is at the core of many problems in model checking, satisfiability checking and program synthesis. Some of the best algorithms for solving parity game are strategy iteration algorithms. These are global in nature since they require the entire parity game to be present at the beginning. This is a distinct disadvantage because in many applications one only needs to know which winning region a particular node belongs to, and a witnessing winning strategy may cover only a fractional part of the entire game graph. We present two local strategy iteration algorithms which explore the game graph on-the-fly whilst performing the improvement steps. We also compare them empirically with existing global strategy iteration algorithms and the currently only other local algorithm for solving parity games. It turns out that local strategy iteration can outperform these others significantly.

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