The complexity of one-agent refinement modal logic

• Authors: Laura Bozzelli;Hans van Ditmarsch;Sophie Pinchinat
• Venue: JELIA'12 Proceedings of the 13th European conference on Logics in Artificial Intelligence
• Year: 2012

We investigate the complexity of satisfiability for one-agent Refinement Modal Logic ($\text{\sffamily RML}$), a known extension of basic modal logic ($\text{\sffamily ML}$) obtained by adding refinement quantifiers on structures. It is known that $\text{\sffamily RML}$ has the same expressiveness as $\text{\sffamily ML}$, but the translation of $\text{\sffamily RML}$ into $\text{\sffamily ML}$ is of non-elementary complexity, and $\text{\sffamily RML}$ is at least doubly exponentially more succinct than $\text{\sffamily ML}$. In this paper, we show that $\text{\sffamily RML}$-satisfiability is 'only' singly exponentially harder than $\text{\sffamily ML}$-satisfiability, the latter being a well-known PSPACE-complete problem. More precisely, we establish that $\text{\sffamily RML}$-satisfiability is complete for the complexity class AEXP$_{\text{\sffamily pol}}$, i.e., the class of problems solvable by alternating Turing machines running in single exponential time but only with a polynomial number of alternations (note that NEXPTIME⊆ AEXP$_{\text{\sffamily pol}}$⊆ EXPSPACE).