The field of circuit complexity is witnessing significant developments, with a focus on compositional control-driven Boolean circuits and constant-depth circuits. Researchers are exploring new models of computation, such as control-driven Boolean circuits, which emerge from the use of colimit-based operators for compositional circuit construction. These models are being shown to be at least as powerful as their classical counterparts, enabling the non-uniform computation of any Boolean function on inputs of arbitrary length. Furthermore, the closure under factorization of algebraic formulas and constant-depth circuits is being established, with applications to the analysis of hitting set generators and the factorization of constant-depth circuits. In the realm of quantum computing, denotational semantics for quantum loops are being proposed, providing a framework for understanding the conceptual meaning of quantum-controlled branching and iteration. Noteworthy papers include:

• Compositional Control-Driven Boolean Circuits, which proposes colimit-based operators for compositional circuit construction.
• Closure under factorization from a result of Furstenberg, which shows that algebraic formulas and constant-depth circuits are closed under taking factors.