Approximate Analysis of Homeostasis of Gene Networks by Linear Temporal Logic using Network Motifs

2015 ◽  
Author(s):  
Sohei Ito ◽  
Shigeki Hagihara ◽  
Naoki Yonezaki
Keyword(s):  
Temporal Logic ◽  
Gene Networks ◽  
Linear Temporal Logic ◽  
Network Motifs ◽  
Approximate Analysis

scholarly journals Modular analysis of gene networks by linear temporal logic

2013 ◽  
Vol 10 (2) ◽  
pp. 12-23 ◽  
Author(s):  
Sohei Ito ◽  
Takuma Ichinose ◽  
Masaya Shimakawa ◽  
Naoko Izumi ◽  
Shigeki Hagihara ◽  
...  
Keyword(s):  
Temporal Logic ◽  
Gene Networks ◽  
Linear Temporal Logic ◽  
Large Network ◽  
Network Analyses ◽  
Modular Analysis ◽  
Modular Method ◽  
Satisfiability Checking ◽  
Computational Difficulty ◽  
High Computational Complexity

Summary Despite a lot of advances in biology and genomics, it is still difficult to utilise such valuable knowledge and information to understand and analyse large biological systems due to high computational complexity. In this paper we propose a modular method with which from several small network analyses we analyse a large network by integrating them. This method is based on the qualitative framework proposed by authors in which an analysis of gene networks is reduced to checking satisfiability of linear temporal logic formulae. The problem of linear temporal logic satisfiability checking needs exponential time in the size of a formula. Thus it is difficult to analyse large networks directly in this method since the size of a formula grows linearly to the size of a network. The modular method alleviates this computational difficulty. We show some experimental results and see how we benefit from the modular analysis method.

scholarly journals Divergent stutter bisimulation abstraction for controller synthesis with linear temporal logic specifications

Automatica ◽  
2021 ◽  
Vol 130 ◽  
pp. 109723
Author(s):  
Sahar Mohajerani ◽  
Robi Malik ◽  
Andrew Wintenberg ◽  
Stéphane Lafortune ◽  
Necmiye Ozay
Keyword(s):  
Temporal Logic ◽  
Linear Temporal Logic ◽  
Controller Synthesis

scholarly journals A Unified Translation of Linear Temporal Logic to ω-Automata

2020 ◽  
Vol 67 (6) ◽  
pp. 1-61
Author(s):  
Javier Esparza ◽  
Jan Křetínský ◽  
Salomon Sickert
Keyword(s):  
Temporal Logic ◽  
Linear Temporal Logic

Extending Linear Temporal Logic with Clocks to Object-Z

2014 ◽  
Vol 513-517 ◽  
pp. 927-930
Author(s):  
Zhi Cheng Wen ◽  
Zhi Gang Chen
Keyword(s):  
Real Time ◽  
Temporal Logic ◽  
Formal Specification ◽  
Large Scale ◽  
Linear Temporal Logic ◽  
Specification Language ◽  
Continuous Variables ◽  
Real Time System ◽  
Software Specification ◽  
Formal Specification Language

Object-Z, an extension to formal specification language Z, is good for describing large scale Object-Oriented software specification. While Object-Z has found application in a number of areas, its utility is limited by its inability to specify continuous variables and real-time constraints. Linear temporal logic can describe real-time system, but it can not deal with time variables well and also can not describe formal specification modularly. This paper extends linear temporal logic with clocks (LTLC) and presents an approach to adding linear temporal logic with clocks to Object-Z. Extended Object-Z with LTLC, a modular formal specification language, is a minimum extension of the syntax and semantics of Object-Z. The main advantage of this extension lies in that it is convenient to describe and verify the complex real-time software specification.

scholarly journals The temporal logic of coalgebras via Galois algebras

2002 ◽  
Vol 12 (6) ◽  
pp. 875-903 ◽  
Author(s):  
BART JACOBS
Keyword(s):  
State Space ◽  
Temporal Logic ◽  
Metric Spaces ◽  
Linear Temporal Logic ◽  
The State ◽  
Temporal Logics ◽  
Computation Tree Logic ◽  
Computation Tree ◽  
Polynomial Functors

This paper introduces a temporal logic for coalgebras. Nexttime and lasttime operators are defined for a coalgebra, acting on predicates on the state space. They give rise to what is called a Galois algebra. Galois algebras form models of temporal logics like Linear Temporal Logic (LTL) and Computation Tree Logic (CTL). The mapping from coalgebras to Galois algebras turns out to be functorial, yielding indexed categorical structures. This construction gives many examples, for coalgebras of polynomial functors on sets. More generally, it will be shown how ‘fuzzy’ predicates on metric spaces, and predicates on presheaves, yield indexed Galois algebras, in basically the same coalgebraic manner.

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