Relations and Its Applications: Difference between revisions

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Created page with "Title: Relations and Its Applications Abstract: This research article explores the existence of an ω-chain for transitive mixed linear relations and its implications for various liveness verification problems. It proposes an approach to verify real-time systems against complex timing requirements using a flattening technique and decidable binary reachability characterizations. The study also discusses the application of these techniques to timed automata augmented with..."
 
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Title: Relations and Its Applications
Title: Relations and Its Applications


Abstract: This research article explores the existence of an ω-chain for transitive mixed linear relations and its implications for various liveness verification problems. It proposes an approach to verify real-time systems against complex timing requirements using a flattening technique and decidable binary reachability characterizations. The study also discusses the application of these techniques to timed automata augmented with discrete counters and pushdown stacks.
Main Research Question: Can we find an efficient method to verify the liveness properties of generalized timed automata?


Main Research Question: Can we automatically verify the existence of an ω-chain for transitive mixed linear relations?
Methodology: The researchers used a unified framework to study liveness verification problems for generalized timed automata. They focused on mixed linear liveness problems and Presburger liveness problems.


Methodology: The research uses a combination of mathematical logic, automata theory, and decision procedures. It employs a recent result of [23] to eliminate quantifiers from the relations and express them into mixed linear constraints. The transitivity of the relations is critical, and removing it from the relations makes the existence of an ω-chain undecidable.
Results: They proved that the mixed linear liveness problem for a timed automaton with dense clocks, reversal-bounded counters, and a free counter is decidable. They also showed that the Presburger liveness problem for a timed automaton with discrete clocks, reversal-bounded counters, and a pushdown stack is decidable.


Results: The main theorem proves that the existence of an ω-chain for transitive mixed linear relations is decidable. This result is applied to the binary reachability of timed automata and pushdown automata, providing a decidable answer to the liveness verification problems.
Implications: These results open up new possibilities for automatic verification of real-time systems against complex timing requirements. They provide a more comprehensive approach to liveness verification problems, which can be applied to various real-world scenarios.


Implications: The research has significant implications for the automatic verification of real-time systems. It opens the door for verifying complex timing requirements and provides a decidable characterization for timed automata and their generalizations. The techniques can be applied to various real-time models, such as timed automata with dense and discrete clocks, and pushdown stacks. This can lead to more accurate and efficient verification of real-time systems, ultimately improving their reliability and safety.
Link to Article: https://arxiv.org/abs/0110063v2
 
Link to Article: https://arxiv.org/abs/0110063v1
Authors:  
Authors:  
arXiv ID: 0110063v1
arXiv ID: 0110063v2


[[Category:Computer Science]]
[[Category:Computer Science]]
[[Category:Relations]]
[[Category:Liveness]]
[[Category:Automata]]
[[Category:Timed]]
[[Category:Research]]
[[Category:Problems]]
[[Category:Existence]]
[[Category:They]]
[[Category:Ω]]
[[Category:Verification]]

Latest revision as of 03:23, 24 December 2023

Title: Relations and Its Applications

Main Research Question: Can we find an efficient method to verify the liveness properties of generalized timed automata?

Methodology: The researchers used a unified framework to study liveness verification problems for generalized timed automata. They focused on mixed linear liveness problems and Presburger liveness problems.

Results: They proved that the mixed linear liveness problem for a timed automaton with dense clocks, reversal-bounded counters, and a free counter is decidable. They also showed that the Presburger liveness problem for a timed automaton with discrete clocks, reversal-bounded counters, and a pushdown stack is decidable.

Implications: These results open up new possibilities for automatic verification of real-time systems against complex timing requirements. They provide a more comprehensive approach to liveness verification problems, which can be applied to various real-world scenarios.

Link to Article: https://arxiv.org/abs/0110063v2 Authors: arXiv ID: 0110063v2

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