# Branching vs. Linear Time: Final Showdown

@inproceedings{Vardi2001BranchingVL, title={Branching vs. Linear Time: Final Showdown}, author={Moshe Y. Vardi}, booktitle={TACAS}, year={2001} }

The discussion of the relative merits of linear- versus branching-time frameworks goes back to early 1980s. One of the beliefs dominating this discussion has been that "while specifying is easier in LTL (linear-temporal logic), verification is easier for CTL (branching-temporal logic)". Indeed, the restricted syntax of CTL limits its expressive power and many important behaviors (e.g., strong fairness) can not be specified in CTL. On the other hand, while model checking for CTL can be done in…

## 293 Citations

CMPT 880 - Computational Logic Linear-time vs. Branching-time Logics

- Computer Science, Philosophy
- 2004

Benefits and drawbacks of each paradigm are discussed in regards to complexity and expressiveness, in model checking and module checking, and it is concluded that there are situations where verification is better suited to a particular temporal framework.

Cooperation, Knowledge, and Time: Alternating-time Temporal Epistemic Logic and its Applications

- Philosophy, Computer ScienceStud Logica
- 2003

The resulting logic — Alternating-time Temporal Epistemic Logic (ATEL) — shares the tractability of model checking with its ATL parent, and is a succinct and expressive language for reasoning about game-like multiagent systems.

Memoryful Branching-Time Logic

- Computer Science21st Annual IEEE Symposium on Logic in Computer Science (LICS'06)
- 2006

It is shown that mCTL* is as expressive, but exponentially more succinct, than CTL*, and that the ability of m CTL* to refer to the present is essential for this equivalence.

Trace Semantics is Fully Abstract

- Computer Science2009 24th Annual IEEE Symposium on Logic In Computer Science
- 2009

This work examines the branching-linear issue from the perspective of process equivalence, which is one of the most fundamental concepts in concurrency theory, as defining a notion of equivalence essentially amounts to defining semantics for processes.

Branching vs. Linear Time: Semantical Perspective

- Computer ScienceATVA
- 2007

This work examines the branching-linear issue from the perspective of process equivalence, which is one of the most fundamental notions in concurrency theory, and postulates three principles that are fundamental to any discussion ofprocess equivalence.

Knowledge , and Time : Alternating-time Temporal Epistemic Logic and its Applications

- Philosophy, Computer Science
- 2003

The resulting logic — Alternating-time Temporal Epistemic Logic (atel) — shares the tractability of model checking with its atl parent, and is a succinct and expressive language for reasoning about game-like multiagent systems.

From Linear to Branching Time in Software Property Specifications

- Computer Science
- 2018

Software verification is a fundamental part of the software development process. Formal verification techniques, such as runtime-monitoring [4] and model checking [1], are based on formal…

Synthesising Classic and Interval Temporal Logic

- Computer Science2011 Eighteenth International Symposium on Temporal Representation and Reasoning
- 2011

The charm of this extension is that PL does not sacrifice the simplicity that makes its sub-logics attractive, and can, by subsuming both interval and classic temporal logics, synthesise both concepts to a common framework.

Temporal Logic and Fair Discrete Systems

- Computer ScienceHandbook of Model Checking
- 2018

This chapter starts with Fair Discrete Structures, the model on which the truth and falsity of temporal logic formulas are evaluated, and introduces Propositional Linear Temporal Logic (LTL), a hybrid of LTL and CTL that combines the linear and branching views into one logic.

Logics for Mazurkiewicz traces

- Computer Science
- 2002

A decision procedure for LTL over Mazurkiewicz traces is exhibited which generalizes the classical automata-theoretic approach to a linear temporal logic interpreted no longer over sequences but restricted labeled partial orders and applies a notion of independencerewriting to formulas of the logic.

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