Core Concepts
Automata Linear Dynamic Logic on Finite Traces (ALDLf) is a temporal logic that extends propositional logic with nondeterministic finite automata (NFA) to express temporal constraints. ALDLf provides greater expressiveness than Linear Temporal Logic on Finite Traces (LTLf) while maintaining PSPACE-completeness for satisfiability checking.
Abstract
The key highlights and insights of this content are:
ALDLf extends the paradigm of Linear Dynamic Logic on Finite Traces (LDLf) by using NFAs instead of regular expressions to express temporal constraints. This provides greater succinctness without increasing the complexity of satisfiability checking.
ALDLf allows for the direct expression of past modalities, in contrast to LDLf which can only make direct claims about the present and future.
The authors introduce a novel variant of the two-way alternating automaton on finite words (2AFW) that uses a Büchi-like acceptance condition to enable the translation of ALDLf formulas to equivalent 2AFWs.
The authors show that satisfiability checking for ALDLf formulas is in PSPACE, the same as for LTLf, despite ALDLf being more expressive (equivalent to Monadic Second-Order Logic) than LTLf (equivalent to Monadic First-Order Logic).
The ALDLf formula to NFA translation procedure can also be used to handle all LDLf formulas, addressing a limitation in the existing LDLf construction where certain formulas can lead to infinite recursion.
The motivation for introducing ALDLf includes the need to express local state, which is not allowed in LDLf, and the theoretical exploration of the succinctness/complexity terrain for finite-horizon temporal logics.