Latticed Simulation Relations and Games

Multi-valued Kripke structures are Kripke structures in which the atomic propositions and the transitions are not Boolean and can take values from some set. In particular, latticed Kripke structures, in which the elements in the set are y ordered, are useful in abstraction, query checking, and reasoning about multiple view-points. The challenges that formal methods involve in the Boolean setting are carried over, and in fact increase, in the presence of multi-valued systems and logics. We lift to the latticed setting two basic notions that have been proven useful in the Boolean setting. We first define latticed simulation between latticed Kripke structures. The relation maps two structures M1 and M2 to a lattice element that essentially denotes the truth value of the statement “every behavior of M1 is also a behavior of M2”. We show that latticed-simulation is logically characterized by the universal fragment of latticed µ-calculus, and can be calculated in polynomial time. We t...

• Type: Conference
• Year: 2007
• Where: ATVA
• Authors: Orna Kupferman, Yoad Lustig
• Keywords: ATVA 2007, Kripke Structures, Latticed Kripke Structures, Multi-valued Kripke Structures