How do theoretical foundations in computer science, such as algorithms, data structures, and complexity theory, underpin the development and advancement of computational systems? Explore how these theoretical frameworks enable the design of efficient algorithms, optimal data storage methods, and scalable solutions for diverse computing challenges. Discuss the role of formal languages and automata theory in modeling computational processes and designing programming languages. Additionally, examine the significance of theoretical concepts like computability and decidability in understanding the limits and capabilities of computing systems. How do these foundational theories influence practical applications across various domains, from software engineering to artificial intelligence?