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(2)
Differential Algebra
Dynamic Logic
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Differentialalgebraic Dynamic Logic for Differentialalgebraic Programs
Differentialalgebraic Dynamic Logic for Differentialalgebraic Programs,10.1093/logcom/exn070,Journal of Logic and Computation,André Platzer
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Differentialalgebraic Dynamic Logic for Differentialalgebraic Programs
(
Citations: 15
)
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André Platzer
Journal:
Journal of Logic and Computation  LOGCOM
, vol. 20, no. 1, pp. 309352, 2010
DOI:
10.1093/logcom/exn070
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The following links allow you to view full publications. These links are maintained by other sources not affiliated with Microsoft Academic Search.
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logcom.oxfordjournals.org
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www.informatik.unitrier.de
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dx.doi.org
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Citation Context
(11)
...Deductive verification of hybrid systems has seen great advancement through a recent series of work by Platzer and his colleagues, including [5,
6
]. Their formalism is variations of dynamic logic, augmented with differential equations to incorporate flowdynamics...
Kohei Suenaga
,
et al.
Programming with Infinitesimals: A WHILELanguage for Hybrid System Mo...
...For example, differentialalgebraic dynamic logic [
17
] due to Platzer was invented by extending dynamic logic with continuous statements...
...Unfortunately, the approaches in [20, 9] were discovered in [28, 27,
17
] to have certain problems with their soundness, if at the boundary of a CI, f is not strictly inward the invariant set...
Jiang Liu
,
et al.
Computing semialgebraic invariants for polynomial dynamical systems
...For this purpose, we present a generalization of differential invariants [
15
, 18, 16]...
...ferential invariant F Differential invariants [
15
, 18, 16] are formulas F that do not change their truthvalue along the dynamics of a differential equation describing a continuous system transition in a hybrid system; see Fig. 2. To prove that F is a differential invariant, it is sufficient to check a condition on the directional derivatives of all terms of the formula [18]...
...plate equations [24, 23], differential invariants [
15
, 18, 16] and a constraintbased template approach [7]...
...For entry, we use a simplified procedure based on what has been used in classical roundabouts [26,
15
]...
...cal proof rules, which we have previously shown to apply to hybrid systems [
15
]...
...We call formula F in rule DI a quantified differential invariant for quantified differential equation ∀ if (i) � = θ & H. Note that stronger assumptions than H are generally unsound for the premiss of DI; see previous work for details [
15
, 16]...
...Without a condition like T (i, j), roundabouts can be unsafe [
15
, 16] so it is crucial that entry establishes it. For a systematic derivation of how to construct T (i, j), we refer to previous work [15, 16]...
...Without a condition like T (i, j), roundabouts can be unsafe [15, 16] so it is crucial that entry establishes it. For a systematic derivation of how to construct T (i, j), we refer to previous work [
15
, 16]...
André Platzer
.
Quantified differential invariants
...In the literature, the Differential Algebraic Dynamic Logic [
8
] can deal with differential equations through differential invariants...
Jiang Liu
,
et al.
A Calculus for Hybrid CSP
...For systems with more complicated differential equations, socalled differential invariants [
5
] can be used to verify properties of differential equations when the solution is unknown or undecidable...
André Platzer
.
Differential Dynamic Logics
References
(10)
Zeno hybrid systems
(
Citations: 72
)
Jun Zhang
,
Karl Henrik Johansson
,
John Lygeros
,
Shankar Sastry
Journal:
International Journal of Robust and Nonlinear Control  INT J ROBUST NONLINEAR CONTR
, vol. 11, no. 5, pp. 435451, 2001
Axioms for realtime logics
(
Citations: 7
)
Pierreyves Schobbens
,
Jeanfrançois Raskin
,
Thomas A. Henzinger
Journal:
Theoretical Computer Science  TCS
, vol. 274, no. 12, pp. 151182, 2002
A Theory of Timed Automata
(
Citations: 2845
)
Rajeev Alur
Journal:
Theoretical Computer Science  TCS
, vol. 126, no. 2, pp. 183235, 1994
Conflict resolution for air traffic management: a study in multiagent hybrid systems
(
Citations: 246
)
Claire Tomlin
,
George J. Pappas
,
Shankar Sastry
Journal:
IEEE Transactions on Automatic Control  IEEE TRANS AUTOMAT CONTR
, vol. 43, no. 4, pp. 509521, 1998
Logics for hybrid systems
(
Citations: 75
)
J. M. Davoren
,
ANIL NERODE
Journal:
Proceedings of The IEEE  PIEEE
, vol. 88, no. 7, pp. 9851010, 2000
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Citations
(15)
Programming with Infinitesimals: A WHILELanguage for Hybrid System Modeling
(
Citations: 1
)
Kohei Suenaga
,
Ichiro Hasuo
Published in 2011.
Computing semialgebraic invariants for polynomial dynamical systems
(
Citations: 1
)
Jiang Liu
,
Naijun Zhan
,
Hengjun Zhao
Published in 2011.
A Complete Method to Polynomial Differential Invariant Generation for Hybrid Systems
Jiang Liu
,
Naijun Zhan
,
Hengjun Zhao
Journal:
Computing Research Repository  CORR
, vol. abs/1102.0, 2011
Quantified differential invariants
André Platzer
Published in 2011.
A Calculus for Hybrid CSP
(
Citations: 2
)
Jiang Liu
,
Jidong Lv
,
Zhao Quan
,
Naijun Zhan
,
Hengjun Zhao
,
Chaochen Zhou
,
Liang Zou
Conference:
Asian Symposium on Programming Languages and Systems  APLAS
, pp. 115, 2010