Fault-tolerant consensus protocols are given for various cases of partial synchrony and various fault models that allow partially synchronous processors to reach some approximately common notion of time.Expand

This paper shows that a number of NP - complete problems remain NP -complete even when their domains are substantially restricted, and determines essentially the lowest possible upper bounds on node degree for which the problems remainNP -complete.Expand

The problem of deciding validity in the theory of equality is shown to be complete in polynomial-space, and close upper and lower bounds on the space complexity of this problem are established.Expand

A number of similar decidable word problems from automata theory and logic whose inherent computational complexity can be precisely characterized in terms of time or space requirements on deterministic or nondeterministic Turing machines are considered.Expand

This paper shows that a number of NP-complete problems remain NP- complete even when their domains are substantially restricted, and determines essentially the lowest possible upper bounds on node degree for which the problems remainNP-complete.Expand

The proofs expose general heuristic principles that explain why consensus is possible in certain models but not possible in others, and several critical system parameters, including various synchronicity conditions, are identified.Expand

This paper is intended to demonstrate the efforts of the Massachusetts Institute of Technology’s graduate students to improve the quality of their teaching and research.Expand

The purpose of this paper is to study reducibilities that can be computed by combinational logic networks of polynomial size and constant depth containing AND’s, OR’s and NOT’s, with no bound placed… Expand