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### Stubborn Sets for Simple Linear Time Properties [chapter]

Andreas Lehmann, Niels Lohmann, Karsten Wolf
2012 Lecture Notes in Computer Science
We contribute a stubborn set approach to simple properties with the following ingredients.  ...  We call a linear time property simple if counterexamples are accepted by a Büchi automaton that has only singleton strongly connected components.  ...  A linear time property is simple iff the set of infinite runs violating the property is accepted by a simple Büchi automaton.  ...

### Stop It, and Be Stubborn!

Antti Valmari
2015 2015 15th International Conference on Application of Concurrency to System Design
If the model is AG EF terminating, then the basic strong stubborn set method preserves safety and some progress properties without any additional condition for solving the ignoring problem.  ...  This publication argues that it is beneficial for both catching non-progress errors and stubborn set state space reduction to try to make verification models AG EF terminating.  ...  The following theorem tells that a well-known simple tool for checking linear-time safety properties works in our context. Theorem 4: Assume that the model is AG EF terminating.  ...

### Page 1034 of Mathematical Reviews Vol. , Issue 93b [page]

1993 Mathematical Reviews
Summary: “We present the LTL preserving stubborn set method for reducing the amount of work needed in the automatic verification of concurrent systems with respect to linear time temporal logic specifications  ...  This representation takes the form of a set of constraints. We show that strictness and full-strictness properties of P can be derived, in a precise and formal sense, from this set of constraints.  ...

### Opinion dynamics with stubborn vertices

Yaokun Wu, Jian Shen
2012 The Electronic Journal of Linear Algebra
The sink vertices in the influence digraph correspond to those stubborn people who never change their opinions.  ...  For example, 225 is a subword of 12345265. Let W be a word over http://math.technion.ac.il/iic/ela Proof of Theorem 1.1.  ...  of the International Linear Algebra Society Volume 23, pp. 790-800, September 2012 ELA Opinion Dynamics With Stubborn Vertices 793 Electronic Journal of Linear Algebra ISSN 1081-3810 A publication  ...

### The social system identification problem

Hoi-To Wai, Anna Scaglione, Amir Leshem
2015 2015 54th IEEE Conference on Decision and Control (CDC)
The stubborn agents opinion is not influenced by the peers they seek to sway, and their opinion bias is the known input to the social network system.  ...  this paper is modeling what we call a Social Radar, i.e. a method to estimate the relative influence between social agents, by sampling their opinions and as they evolve, after injecting in the network stubborn  ...  The final opinions are driven by the initial opinions at the stubborn agents. Importantly, Eq. (7) gives a set of linear equations that characterizes the social system S.  ...

### On-the-fly verification with stubborn sets [chapter]

Antti Valmari
1993 Lecture Notes in Computer Science
A simple algorithm is Suggested for efficient detection of violations of an important subclass of liveness properties during the construction of the reduced state space.  ...  To reduce the number of states that are constructed the method applies the stubborn set theory in a new way. The method can be used in connection with the "Supertrace" memory-saving technique.  ...  Thirdly, we present a simple algorithm for checking certain liveness properties.  ...

### The Influence of Stubborn Agents in a Multi-Agent Network for Inter-Team Cooperation/Negotiation

Eugene S., Akira Namatame
2015 International Journal of Advanced Research in Artificial Intelligence (IJARAI)
In this paper, a multi-agent system is used under the restrain of a network structure to model two teams of agents interacting for a common consensus, however with the presence of stubborn agents.  ...  When teams interact for cooperation or negotiation, there are unique dynamics that occur depending on the conditions.  ...  which are linear interpolations of the two stubborn agents' beliefs.  ...

### Stubborn state observers for linear time-invariant systems

Angelo Alessandri, Luca Zaccarian
2018 Automatica
For the purpose of estimating the state of a linear time-invariant system with measurements subject to outliers, we propose an observer with a saturated output injection in such a way to mitigate the effect  ...  Stability conditions in both the continuous-time and the discrete-time cases are derived, which ensure global exponential stability to the origin for the error dynamics.  ...  For such reasons, this additional constraint does not restrict the feasibility set. Full stubborn (FS) design.  ...

### Supporting domain-specific state space reductions through local partial-order reduction

Peter Bokor, Johannes Kinder, Marco Serafini, Neeraj Suri
2011 2011 26th IEEE/ACM International Conference on Automated Software Engineering (ASE 2011)
LPOR is based on the existing notion of statically computed stubborn sets, but its locality allows to verify conditions in single states rather than over long paths.  ...  Model checkers offer to automatically prove safety and liveness properties of complex concurrent software systems, but they are limited by state space explosion.  ...  We thank Gerard Holzmann for his insights of the POR theory as implemented by SPIN to enable an objective comparison across LPOR and SPIN.  ...

### Guard-Based Partial-Order Reduction [chapter]

Alfons Laarman, Elwin Pater, Jaco van de Pol, Michael Weber
2013 Lecture Notes in Computer Science
Our starting point is the stubborn set algorithm of Valmari (see also Godefroid's thesis), which relies on necessary enabling sets.  ...  While the reductions take longer, they are consistently better than Spin's ample set and even often surpass the ideal upper bound for the ample set, as established empirically by Geldenhuys, Hansen and  ...  We are grateful to Antti Valmari, Patrice Godefroid and Dragan Bošnački for their useful feedback on this paper.  ...

### On combining the stubborn set method with the sleep set method [chapter]

Kimmo Varpaaniemi
1994 Lecture Notes in Computer Science
Both methods can be extended to verify properties expressed as linear temporal logic formulae as shown by Valmari 18, 20, 21], Wolper and Godefroid 24], and Peled 13].  ...  The presentation does not go beyond what is necessary for the remaining sections. In Section 3, dynamically stubborn sets 14, 19] are shown to be a useful generalization of stubborn sets.  ...  I am grateful to Professor Leo Ojala for his continuous support, and Acting Associate Professor Mikko Tiusanen and Associate Professor Antti Valmari for their helpful comments.  ...

### NAIRU Uncertainty and Nonlinear Policy Rules

Laurence H Meyer, Eric T Swanson, Volker W Wieland
2001 The American Economic Review
This policy displays the usual property of certainty-equivalence: interest * Meyer and Swanson: Federal Reserve Board, 20th and Constitution Ave., N.W.,  ...  Optimal policy in this standard linear-quadratic model is then given by (3) r t ϭ r* ϩ a͑ t Ϫ *͒ Ϫ b͑u t Ϫ E t u*͒ where we assume that policymakers control the real interest rate r t .  ...  than the simple linear rule, because policymakers tend to arrive more quickly at a correct estimate for u*.  ...

### NAIRU Uncertainty and Nonlinear Policy Rules

Laurence H. Meyer, Eric T. Swanson, Volker Wieland
2001 Social Science Research Network
This policy displays the usual property of certainty-equivalence: interest * Meyer and Swanson: Federal Reserve Board, 20th and Constitution Ave., N.W.,  ...  Optimal policy in this standard linear-quadratic model is then given by (3) r t ϭ r* ϩ a͑ t Ϫ *͒ Ϫ b͑u t Ϫ E t u*͒ where we assume that policymakers control the real interest rate r t .  ...  than the simple linear rule, because policymakers tend to arrive more quickly at a correct estimate for u*.  ...

### Page 5009 of Mathematical Reviews Vol. , Issue 2001G [page]

2001 Mathematical Reviews
reductions for universal branching time properties (245- 267); James F.  ...  of CTL (331-341); Kay Schréter, Gabriela Lindemann-v.Trzebiatowski and Lutz Fritsche, TBase2—a web-based electronic patient record (343-353); Kimmo Varpaaniemi, Stable models for stubborn sets (355-375  ...

### Results on stubborn Luenberger observers for linear time-invariant plants

A. Alessandri, L. Zaccarian
2015 2015 European Control Conference (ECC)
We address the problem of constructing asymptotic observers for linear time-invariant systems with measurements subject to outliers.  ...  Such conditions can be employed for optimal parameter selection by using linear matrix inequalities. The effectiveness of the approach is shown by means of some numerical examples. A.  ...  Moreover, we set σ(0) equal to zero in the stubborn observers. A.  ...
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