The field of theoretical computer science is moving towards a deeper understanding of the underlying structures and semantics of programming languages and automata. Researchers are exploring new approaches to modeling and analyzing complex systems, including the use of homological invariants, categorical frameworks, and algebraic theories. Noteworthy papers in this area include the introduction of Ohana trees for the λI-calculus, which provides a new perspective on the evaluation of lambda terms, and the development of a cyclic proof system for alternating parity automata, which offers a novel approach to verifying the correctness of infinite-state systems. Other notable works include the extension of the B"uchi-Elgot-Trakhtenbrot Theorem to higher-dimensional automata and the introduction of a categorical and logical framework for iterated protocols.
New Developments in Theoretical Computer Science
Sources
Ohana trees and Taylor expansion for the $\lambda$I-calculus. No variable gets left behind or forgotten!
The $K_\infty$ Homotopy $\lambda$-Model
Reflexive Composition of Elementary State Machines, with an Application to the Reversal of Cellular Automata Rule 90
Cyclic system for an algebraic theory of alternating parity automata
Initial Algebra Correspondence under Reachability Conditions
Phase Transitions in Decision Problems Over Odd-Sized Alphabets
A categorical and logical framework for iterated protocols
Homological Invariants of Higher-Order Equational Theories
B\"uchi-Elgot-Trakhtenbrot Theorem for Higher-Dimensional Automata