An n log n Algorithm for Online BDD Refinement

Binary Decision Diagrams are in widespread use in verification systemsfor the canonical representation of Boolean functions. A BDD representinga function phi : B^nu -> N can easily be reduced to its canonical form inlinear time.In this paper, we consider a natural online BDD refinement problemand show that it can be solved in O(n log n) if n bounds the size of theBDD and the total size of update operations.We argue that BDDs in an algebraic framework should be understoodas minimal fixed points superimposed on maximal fixed points. We proposea technique of controlled growth of equivalence classes to make theminimal fixed point calculations be carried out efficiently. Our algorithmis based on a new understanding of the interplay between the splittingand growing of classes of nodes.We apply our algorithm to show that automata with exponentiallylarge, but implicitly represented alphabets, can be minimized in timeO(n log n), where n is the total number of BDD nodes representing theautomaton

The Origins of Racism: The Critical Theory of Oliver C. Cox

Oliver C. Cox's theory of race relations and its impending problems in connection with the rise of capitalism have not been applied or addressed to the same extent as that of his contemporaries. Why does the work of Oliver Cox continue to be largely ignored and set aside? We will first look at Cox's hypothesis and some of the concepts he uses, his argument regarding the genesis of racism, and his criticisms of some of his better known contemporaries that may well have contributed to the bitter relationships he encountered

BDD Algortihms and Cache Misses

Within the last few years, CPU speed has greatly overtaken memory speed. For this reason, implementation of symbolic algorithms - with their extensive use of pointers and hashing - must be reexamined. In this paper, we introduce the concept of cache miss complexityas an analytical tool for evaluating algorithms depending on pointer chasing. Such algorithms are typical of symbolic computation found in verification. We show how this measure suggests new data structures and algorithmsfor multi-terminal BDDs. Our ideas have been implemented ina BDD package, which is used in a decision procedure for the Monadic Second-order Logic on strings.Experimental results show that on large examples involving e.g the verification of concurrent programs, our implementation runs 4 to 5 times faster than a widely used BDD implementation.We believe that the method of cache miss complexity is of general interest to any implementor of symbolic algorithms used in verification

Exercise as a Mean to Control Low-Grade Systemic Inflammation

Chronic noncommunicable diseases (CNCDs), which include cardiovascular disease, some cancers, for example, colon cancer, breast cancer, and type 2 diabetes, are reaching epidemic proportions worldwide. It has now become clear that low-grade chronic inflammation is a key player in the pathogenesis of most CNCDs. Given that regular exercise offers protection against all causes of mortality, primarily by protection against atherosclerosis and insulin resistance, we suggest that exercise may exert some of its beneficial health effects by inducing anti-inflammatory actions. Recently, IL-6 was introduced as the first myokine, defined as a cytokine, which is produced and released by contracting skeletal muscle fibres, exerting its effects in other organs of the body. We suggest that skeletal muscle is an endocrine organ and that myokines may be involved in mediating the beneficial effects against CNCDs associated with low-grade inflammation

Automated Logical Verification based on Trace Abstractions

We propose a new and practical framework for integrating the behavioralreasoning about distributed systems with model-checking methods.Our proof methods are based on trace abstractions, which relate thebehaviors of the program and the specification. We show that for finite-statesystems such symbolic abstractions can be specified conveniently inMonadic Second-Order Logic (M2L). Model-checking is then made possibleby the reduction of non-determinism implied by the trace abstraction.Our method has been applied to a recent verification problem by Broyand Lamport. We have transcribed their behavioral description of a distributedprogram into temporal logic and verified it against another distributedsystem without constructing the global program state space. Thereasoning is expressed entirely within M2L and is carried out by a decisionprocedure. Thus M2L is a practical vehicle for handling complex temporallogic specifications, where formulas decided by a push of a button are aslong as 10-15 pages