A model of computation for which reasonable yet still incomplete lower bounds are known is the read-once branching program. Here variants of complexity measures successful in the study of read-once branching programs are defined and studied. Some new or simpler proofs of known bounds are uncovered. Branching program resources and the new measures are compared extensively. The new variants are developed in part in the hope of tackling read-k branching programs for the tree evaluation problem studied in Cook et al. Other computation problems are studied as well. In particular, a common view of a function studied by Gal and a function studied by Bollig and Wegener leads to the general combinatorics of blocking sets. Technical combinatorial results of independent interest are obtained. New leads towards further progress are discussed. An exponential lower bound for non-deterministic read-k branching programs for the GEN function is also derived, independently from the new measures.

翻译：已知一种计算模型——一次性分支程序，虽已获得合理但尚不完整的下界。本文定义并研究了在一次性分支程序研究中行之有效的复杂度度量的变体，揭示了已知界的一些新证明或简化证明，并对分支程序资源与新度量进行了全面比较。新变体的部分发展旨在解决Cook等人研究的树评估问题中的k次读取分支程序，同时研究了其他计算问题。特别地，通过对Gal研究的函数与Bollig和Wegener研究的函数的统一视角，引出了阻塞集的一般组合学，并获得了具有独立意义的技术性组合结果。文中讨论了推动进一步研究的新方向，并独立于新度量，推导了GEN函数的非确定性k次读取分支程序的指数级下界。