Propositional dynamic logic of context-free programs

1981 ◽  
Author(s):  
David Harel ◽  
Amir Pnueli ◽  
Jonathan Stavi
Keyword(s):  
Dynamic Logic ◽  
Propositional Dynamic Logic ◽  
Context Free

scholarly journals Temporal Logics Beyond Regularity

2007 ◽  
Vol 14 (13) ◽  
Author(s):  
Martin Lange
Keyword(s):  
Model Checking ◽  
Dynamic Logic ◽  
Expressive Power ◽  
Turing Machines ◽  
Temporal Logics ◽  
Propositional Dynamic Logic ◽  
Program Correctness ◽  
Recursive Procedures ◽  
Language Classes ◽  
Context Free

Non-regular program correctness properties play an important role in the specification of unbounded buffers, recursive procedures, etc. This thesis surveys results about the relative expressive power and complexity of temporal logics which are capable of defining non-regular properties. In particular, it features Propositional Dynamic Logic of Context-Free Programs, Fixpoint Logic with Chop, the Modal Iteration Calculus, and Higher-Order Fixpoint Logic.<br /> <br />Regarding expressive power we consider two classes of structures: arbitrary transition systems as well as finite words as a subclass of the former. The latter is meant to give an intuitive account of the logics' expressive powers by relating them to known language classes defined in terms of grammars or Turing Machines. <br /> <br /> Regarding the computational complexity of temporal logics beyond regularity we focus on their model checking problems since their satisfiability problems are all highly undecidable. Their model checking complexities range between polynomial time and non-elementary.

scholarly journals Dynamic Linear Time Temporal Logic

1997 ◽  
Vol 4 (8) ◽  
Author(s):  
Jesper G. Henriksen ◽  
P. S. Thiagarajan
Keyword(s):  
Temporal Logic ◽  
Linear Time ◽  
Dynamic Logic ◽  
Order Theory ◽  
Simple Extension ◽  
Propositional Dynamic Logic ◽  
First Order ◽  
Time Semantics ◽  
Linear Time Temporal Logic ◽  
Obvious Manner

A simple extension of the propositional temporal logic of linear<br />time is proposed. The extension consists of strengthening the until<br />operator by indexing it with the regular programs of propositional<br />dynamic logic (PDL). It is shown that DLTL, the resulting logic, is<br />expressively equivalent to S1S, the monadic second-order theory<br />of omega-sequences. In fact a sublogic of DLTL which corresponds<br />to propositional dynamic logic with a linear time semantics is<br />already as expressive as S1S. We pin down in an obvious manner<br />the sublogic of DLTL which correponds to the first order fragment<br />of S1S. We show that DLTL has an exponential time decision<br />procedure. We also obtain an axiomatization of DLTL. Finally,<br />we point to some natural extensions of the approach presented<br />here for bringing together propositional dynamic and temporal<br />logics in a linear time setting.

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