## Automated Symbolic Reachability Analysis; with Application to Delta-Notch Signaling Automata (2003)

### Cached

### Download Links

- [cherokee.stanford.edu]
- [www.csl.sri.com]
- [arl.stanford.edu]
- [sun-valley.stanford.edu]
- DBLP

### Other Repositories/Bibliography

Venue: | Lecture Notes in Computer Science |

Citations: | 29 - 2 self |

### BibTeX

@INPROCEEDINGS{Ghosh03automatedsymbolic,

author = {Ronojoy Ghosh and Ashish Tiwari and Claire Tomlin},

title = {Automated Symbolic Reachability Analysis; with Application to Delta-Notch Signaling Automata},

booktitle = {Lecture Notes in Computer Science},

year = {2003},

pages = {233--248},

publisher = {Springer-Verlag}

}

### OpenURL

### Abstract

This paper describes the implementation of predicate abstraction techniques to automatically compute symbolic backward reachable sets of high dimensional piecewise a#ne hybrid automata, used to model Delta-Notch biological cell signaling networks. These automata are analyzed by creating an abstraction of the hybrid model, which is a finite state discrete transition system, and then performing the computation on the abstracted system. All the steps, from model generation to the simplification of the reachable set, have been automated using a variety of decision procedure and theorem-proving tools. The concluding example computes the reach set for a four cell network with 8 continuous and 256 discrete states. This demonstrates the feasibility of using these tools to compute on high dimensional hybrid automata, to provide deeper insight into realistic biological systems.

### Citations

599 | Construction of abstract state graphs with PVS - Graf, Saïdi - 1997 |

563 |
A decision method for elementary algebra and geometry
- Tarski
- 1948
(Show Context)
Citation Context ...ty (see, for example [21]). The process of construction of the abstract system requires logical reasoning in the theory of reals. The first-order theory of real closed fields is known to be decidable =-=[23]-=- and the first practical algorithm, based on cylindrical algebraic decomposition, was given in [8], which has gone through several improvements [13, 17]. We use the first-order theory of reals to repr... |

424 | Modeling and simulation of genetic regulatory systems: a literature review
- Jong
(Show Context)
Citation Context ... [12,20], polyhedral representations [3,7], piecewise affine systems [4], ellipsoidal approximations [6], and projections of convergent approximations [18,19]. Recently, qualitative simulation models =-=[14,15]-=- have been proposed to abstract continuous phase portraits of hybrid automata to simpler transition graphs, on which reachability analysis can be performed. Predicate abstraction [1,11] and quantifier... |

356 | HyTech: A Model Checker for Hybrid Systems
- Henzinger, Ho, et al.
- 1997
(Show Context)
Citation Context ...ere has been a recent research focus on techniques which use approximations of various types to make the problem of computing reachable sets tractable; these include the use of linear hybrid automata =-=[12,20]-=-, polyhedral representations [3,7], piecewise affine systems [4], ellipsoidal approximations [6], and projections of convergent approximations [18,19]. Recently, qualitative simulation models [14,15] ... |

122 |
Quantifier elimination for the elementary theory of real closed fields by cylindrical algebraic decomposition
- Collins
- 1975
(Show Context)
Citation Context ...soning in the theory of reals. The first-order theory of real closed fields is known to be decidable [23] and the first practical algorithm, based on cylindrical algebraic decomposition, was given in =-=[8]-=-, which has gone through several improvements [13, 17]. We use the first-order theory of reals to represent sets of continuous states and use reasoning over this theory for creating the abstract trans... |

59 |
Verification of hybrid systems with linear differential inclusions using ellipsoidal approximations
- Botchkarev, Tripakis
- 2000
(Show Context)
Citation Context ... the problem of computing reachable sets tractable; these include the use of linear hybrid automata [12,20], polyhedral representations [3,7], piecewise affine systems [4], ellipsoidal approximations =-=[6]-=-, and projections of convergent approximations [18,19]. Recently, qualitative simulation models [14,15] have been proposed to abstract continuous phase portraits of hybrid automata to simpler transiti... |

58 | Series of abstractions for hybrid automata
- Tiwari, Khanna
- 2002
(Show Context)
Citation Context ...oposed to abstract continuous phase portraits of hybrid automata to simpler transition graphs, on which reachability analysis can be performed. Predicate abstraction [1,11] and quantifier elimination =-=[24]-=- have been proposed for computing discrete abstractions of hybrid automata. Predicate abstraction provides a means for combining theorem proving and model checking techniques by automatically mapping ... |

51 | Lateral inhibition through delta-notch signaling: a piecewise affine hybrid model
- Ghosh, Tomlin
- 2001
(Show Context)
Citation Context ...ns for high-dimensional (in both continuous and discrete variables) hybrid automata with multiple equilibria. The motivating example is the Delta-Notch cell signaling system described and analyzed in =-=[10]. -=-The ⋆ This research is supported by the DARPA Bio:Info:Micro program, grant MDA97200-1-0032, and the DARPA BioSpice program under contract DE-AC03-765F00098. O. Maler and A. Pnueli (Eds.): HSCC 2003... |

44 | Reachability analysis of hybrid systems via predicate abstraction
- Alur, Dang, et al.
(Show Context)
Citation Context ...lation models [14,15] have been proposed to abstract continuous phase portraits of hybrid automata to simpler transition graphs, on which reachability analysis can be performed. Predicate abstraction =-=[1,11]-=- and quantifier elimination [24] have been proposed for computing discrete abstractions of hybrid automata. Predicate abstraction provides a means for combining theorem proving and model checking tech... |

44 |
An improved projection operation for cylindrical algebraic decomposition
- McCallum
- 1998
(Show Context)
Citation Context ...eory of real closed fields is known to be decidable [23] and the first practical algorithm, based on cylindrical algebraic decomposition, was given in [8], which has gone through several improvements =-=[13, 17]-=-. We use the first-order theory of reals to represent sets of continuous states and use reasoning over this theory for creating the abstract transition system. 4.1 Abstraction Process The abstraction ... |

39 | An overview of SAL
- Bensalem, Ganesh, et al.
- 2000
(Show Context)
Citation Context ... in the previous section are included in the SAL model. 3.1 The SAL Modeling Language Hybrid systems described in terms of interacting hybrid automata can be specified using the SAL modeling language =-=[5,9]-=-. Here we shall only describe those features of the SAL modeling language that will be used in the specification of the Delta-Notch signaling mechanism. A SAL specification consists of module definiti... |

38 |
An improvement of the projection operator in cylindrical algebraic decomposition
- Hong
- 1990
(Show Context)
Citation Context ...cess, from generating the SAL model for an arbitrarily large cell network, to obtaining the final reachable sets, is completely automated using MATLAB code written by us, the SAL tool set, and QEPCAD =-=[13]-=- (Quantifier Elimination by Partial Cylindrical Algebraic Decomposition), which is used to simplify the formula defining the reachable set. However, some analysis necessary to generate the parameter c... |

35 |
Application of level set methods to control and reachability problems in continuous and hybrid systems
- Mitchell
(Show Context)
Citation Context ...; these include the use of linear hybrid automata [12,20], polyhedral representations [3,7], piecewise affine systems [4], ellipsoidal approximations [6], and projections of convergent approximations =-=[18,19]-=-. Recently, qualitative simulation models [14,15] have been proposed to abstract continuous phase portraits of hybrid automata to simpler transition graphs, on which reachability analysis can be perfo... |

31 | Overapproximating reachable sets by HamiltonJacobi projections
- Mitchell, Tomlin
- 2003
(Show Context)
Citation Context ...; these include the use of linear hybrid automata [12,20], polyhedral representations [3,7], piecewise affine systems [4], ellipsoidal approximations [6], and projections of convergent approximations =-=[18,19]-=-. Recently, qualitative simulation models [14,15] have been proposed to abstract continuous phase portraits of hybrid automata to simpler transition graphs, on which reachability analysis can be perfo... |

29 | Optimization-based verification and stability characterization of piecewise affine and hybrid systems
- Bemporad, Torrisi, et al.
(Show Context)
Citation Context ...mations of various types to make the problem of computing reachable sets tractable; these include the use of linear hybrid automata [12,20], polyhedral representations [3,7], piecewise affine systems =-=[4]-=-, ellipsoidal approximations [6], and projections of convergent approximations [18,19]. Recently, qualitative simulation models [14,15] have been proposed to abstract continuous phase portraits of hyb... |

22 | Proving properties of continuous systems: qualitative simulation and temporal logic
- Shults, Kuipers
- 1997
(Show Context)
Citation Context ...on. This basic idea, although in a muchs240 R. Ghosh, A. Tiwari, and C. Tomlin simplified form, is also at the core of qualitative reasoning techniques developed in the AI community (see, for example =-=[21]-=-). The process of construction of the abstract system requires logical reasoning in the theory of reals. The first-order theory of real closed fields is known to be decidable [23] and the first practi... |

17 |
B.: Verification of infinite-state dynamic systems using approximate quotient transition systems
- Chutinan, Krogh
(Show Context)
Citation Context ... on techniques which use approximations of various types to make the problem of computing reachable sets tractable; these include the use of linear hybrid automata [12,20], polyhedral representations =-=[3,7]-=-, piecewise affine systems [4], ellipsoidal approximations [6], and projections of convergent approximations [18,19]. Recently, qualitative simulation models [14,15] have been proposed to abstract con... |

13 | Delta-notch lateral inhibitory patterning in the emergence of ciliated cells in Xenopus: experimental observations and a gene network model
- Marnellos, Deblandre, et al.
- 2000
(Show Context)
Citation Context ...oduce less. The Delta-Notch signaling mechanism has been found to cause pattern formation in many different biological systems, such as the South African clawtoed frog (Xenopus laevis) embryonic skin =-=[16] stu-=-died here. An example of the distinctive “salt-and-pepper” pattern formed due to lateral inhibition is in the Xenopus epidermal layer where a regular set of ciliated cells form within a matrix of ... |

8 | A hybrid systems approach to modeling and analyzing planar cell polarity - Amonlirdviman, Ghosh, et al. - 2002 |

8 | Qualitative modeling and heterogeneous control of global system behavior
- Kuipers, Ramamoorthy
- 2002
(Show Context)
Citation Context ... [12,20], polyhedral representations [3,7], piecewise affine systems [4], ellipsoidal approximations [6], and projections of convergent approximations [18,19]. Recently, qualitative simulation models =-=[14,15]-=- have been proposed to abstract continuous phase portraits of hybrid automata to simpler transition graphs, on which reachability analysis can be performed. Predicate abstraction [1,11] and quantifier... |

7 |
d/dt: A verification tool for hybrid systems
- Asarin, Dang, et al.
(Show Context)
Citation Context ... on techniques which use approximations of various types to make the problem of computing reachable sets tractable; these include the use of linear hybrid automata [12,20], polyhedral representations =-=[3,7]-=-, piecewise affine systems [4], ellipsoidal approximations [6], and projections of convergent approximations [18,19]. Recently, qualitative simulation models [14,15] have been proposed to abstract con... |

7 | Qualitative modeling of hybrid systems - Sokolsky, Hong - 2001 |

3 |
A procedure for reachability analysis of rectangular automata
- Preußig, Wong-Toi
- 2000
(Show Context)
Citation Context ...ere has been a recent research focus on techniques which use approximations of various types to make the problem of computing reachable sets tractable; these include the use of linear hybrid automata =-=[12,20]-=-, polyhedral representations [3,7], piecewise affine systems [4], ellipsoidal approximations [6], and projections of convergent approximations [18,19]. Recently, qualitative simulation models [14,15] ... |