Mathematical Models behind the Five Year Plans

Mathematical models have been used to spell out development priorities and determine sectoral growth profiles in the Five Year Plans. The models used in the pre-reform period belong to the family of growth and investment model. This chapter discusses the basic features of the Mahalanobis model, which was used in the Second Plan, and describes the manner in which input–output based consistency models were used in the Fifth to the Eighth Plans. It gives an overview of the macroeconomic model and input–output model used in Plan formulation in the period of economic reform. The idea is to enable the general readers to be acquinted with the manner and method of employing these models in different stages of Plan formulation, and to understand how intuitively the targets in different areas and sectors of the economy are fixed.

Checking Robustness Between Weak Transactional Consistency Models

Concurrent accesses to databases are typically encapsulated in transactions in order to enable isolation from other concurrent computations and resilience to failures. Modern databases provide transactions with various semantics corresponding to different trade-offs between consistency and availability. Since a weaker consistency model provides better performance, an important issue is investigating the weakest level of consistency needed by a given program (to satisfy its specification). As a way of dealing with this issue, we investigate the problem of checking whether a given program has the same set of behaviors when replacing a consistency model with a weaker one. This property known as robustness generally implies that any specification of the program is preserved when weakening the consistency. We focus on the robustness problem for consistency models which are weaker than standard serializability, namely, causal consistency, prefix consistency, and snapshot isolation. We show that checking robustness between these models is polynomial time reducible to a state reachability problem under serializability. We use this reduction to also derive a pragmatic proof technique based on Lipton’s reduction theory that allows to prove programs robust. We have applied our techniques to several challenging applications drawn from the literature of distributed systems and databases.