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    STUDIA INFORMATICA - Issue no. 1 / 2009  
         
  Article:   PROVING THE DECIDABILITY OF THE PDL×PDL PRODUCT LOGIC.

Authors:  LÁSZLÓ ASZALÓS, PHILIPPE BALBIANI.
 
       
         
  Abstract:  The propositional dynamic logic (PDL) is an adequate tool to write down programs. In a previous article we used PDL to formulate cryptographic protocols as parallel programs. In these protocols at least two agents/individuals exchange messages, so we needed to use product logic to formulate the parallel actions. Ágnes Kurucz proved that S5×S5×S5 – which is the simplest triple product logic – is undecidable, hence it follows that PDL×PDL×PDL is undecidable, too. It is easy to show that the PDL logic (without the star operator) is decidable, so it is an interesting problem, that the PDL×PDL product logic is decidable or not.

Key words and phrases. Mathematical logic, Decidability, PDL×PDL product logic, Formal verification.


 
         
     
         
         
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