Advances in Logical Frameworks and Automata

The field of logical frameworks and automata is witnessing significant developments, with a focus on extending existing frameworks to accommodate modal logic, game logic, and differential equations. Researchers are exploring new approaches to equivalence checking, decision procedures, and constraint solving, leading to improved efficiency and expressiveness. Notable advancements include the alignment of expressive and deductive power between different logical systems, the development of efficient algorithms for tree automata, and the introduction of novel decision procedures for string constraints. Noteworthy papers include: Complete First-Order Game Logic, which proves the equiexpressiveness and equivalence of first-order game logic and the first-order modal mu-calculus. A Uniform Framework for Handling Position Constraints in String Solving, which introduces a novel decision procedure for solving position string constraints, leading to significant efficiency gains. On the Equivalence Checking Problem for Deterministic Top-Down Tree Automata, which presents an efficient algorithm for checking language equivalence of states in top-down deterministic finite tree automata.

Sources

First-Order Modal Logic via Logical Categories

An Extended Symbolic-Arithmetic Model for Teaching Double-Black Removal with Rotation in Red-Black Trees

Complete First-Order Game Logic

On the Equivalence Checking Problem for Deterministic Top-Down Tree Automata

A Uniform Framework for Handling Position Constraints in String Solving (Technical Report)

Built with on top of