A Computational Theory of Software Complexity for Distributed Ledger Applications in African Financial Markets

Distributed ledger technology (DLT) is being adopted across African financial markets for securities settlement, cross-border payments, and microfinance platforms, yet the computational complexity characteristics of DLT software in resource-constrained African financial infrastructure contexts remain theoretically underdeveloped. This dissertation develops a computational theory of software complexity for distributed ledger applications in African financial markets, with primary empirical grounding in Nigeria's nascent DLT financial ecosystem spanning the Lagos-Abuja corridor. A formal theory construction methodology is employed, combining mathematical modelling, systematic literature review, and empirical validation. Phase one reviews DLT consensus mechanism complexity theory, CAP theorem applications to financial DLT, and transaction finality theory across Hyperledger Fabric, Ethereum, and Corda platforms. Phase two develops a formal complexity model, the African Financial DLT Complexity Index (AFDCI), incorporating novel complexity dimensions absent from existing models: intermittent consensus node availability (modelling Nigerian network partition patterns), regulatory-induced transaction rollback complexity, and multi-currency denomination handling complexity specific to African cross-border payment use cases. Phase three validates AFDCI empirically through instrumented DLT deployments at three Nigerian financial institutions, measuring complexity growth trajectories across transaction volume scaling, consensus node dropout simulation, and regulatory reporting event triggers. Phase four conducts mathematical proof verification of three AFDCI theoretical propositions using Isabelle/HOL. The dissertation contributes a validated formal complexity theory and measurement instrument for DLT in African financial software systems. Keywords: distributed ledger, computational complexity, African financial markets, Nigeria, blockchain theory