Geometric Random Inner Products: A New Family of Tests for Random Number Generators

We present a new computational scheme, GRIP (Geometric Random Inner Products), for testing the quality of random number generators. The GRIP formalism utilizes geometric probability techniques to calculate the average scalar products of random vectors generated in geometric objects, such as circles and spheres. We show that these average scalar products define a family of geometric constants which can be used to evaluate the quality of random number generators. We explicitly apply the GRIP tests to several random number generators frequently used in Monte Carlo simulations, and demonstrate a new statistical property for good random number generators

Stateful Testing: Finding More Errors in Code and Contracts

Automated random testing has shown to be an effective approach to finding faults but still faces a major unsolved issue: how to generate test inputs diverse enough to find many faults and find them quickly. Stateful testing, the automated testing technique introduced in this article, generates new test cases that improve an existing test suite. The generated test cases are designed to violate the dynamically inferred contracts (invariants) characterizing the existing test suite. As a consequence, they are in a good position to detect new errors, and also to improve the accuracy of the inferred contracts by discovering those that are unsound. Experiments on 13 data structure classes totalling over 28,000 lines of code demonstrate the effectiveness of stateful testing in improving over the results of long sessions of random testing: stateful testing found 68.4% new errors and improved the accuracy of automatically inferred contracts to over 99%, with just a 7% time overhead.Comment: 11 pages, 3 figure

On the Design of LIL Tests for (Pseudo) Random Generators and Some Experimental Results

NIST SP800-22 (2010) proposes the state of art testing suite for (pseudo) random generators to detect deviations of a binary sequence from randomness. On the one hand, as a counter example to NIST SP800-22 test suite, it is easy to construct functions that are considered as GOOD pseudorandom generators by NIST SP800-22 test suite though the output of these functions are easily distinguishable from the uniform distribution. Thus these functions are not pseudorandom generators by definition. On the other hand, NIST SP800-22 does not cover some of the important laws for randomness. Two fundamental limit theorems about random binary strings are the central limit theorem and the law of the iterated logarithm (LIL). Several frequency related tests in NIST SP800-22 cover the central limit theorem while no NIST SP800-22 test covers LIL. This paper proposes techniques to address the above challenges that NIST SP800-22 testing suite faces. Firstly, we propose statistical distance based testing techniques for (pseudo) random generators to reduce the above mentioned Type II errors in NIST SP800-22 test suite. Secondly, we propose LIL based statistical testing techniques, calculate the probabilities, and carry out experimental tests on widely used pseudorandom generators by generating around 30TB of pseudorandom sequences. The experimental results show that for a sample size of 1000 sequences (2TB), the statistical distance between the generated sequences and the uniform distribution is around 0.07 (with $0$ for statistically indistinguishable and $1$ for completely distinguishable) and the root-mean-square deviation is around 0.005

Stock Repurchase Agreements: Close Corporation Use of Designee Provision Permits Repurchase Despite Insufficient Earned Surplus

Statistical random number testing is a well studied field focusing on pseudo-random number generators, that is to say algorithms that produce random-looking sequences of numbers. These generators tend to have certain kinds of flaws, which have been exploited through rigorous testing. Such testing has led to advancements, and today pseudo random number generators are both very high-speed and produce seemingly random numbers. Recent advancements in quantum physics have opened up new doors, where products called quantum random number generators that produce acclaimed true randomness have emerged. Of course, scientists want to test such randomness, and turn to the old tests used for pseudo random number generators to do this. The main question this thesis seeks to answer is if publicly available such tests are good enough to evaluate a quantum random number generator. We also seek to compare sequences from such generators with those produced by state of the art pseudo random number generators, in an attempt to compare their quality. Another potential problem with quantum random number generators is the possibility of them breaking without the user knowing. Such a breakdown could have dire consequences. For example, if such a generator were to control the output of a slot machine, an malfunction could cause the machine to generate double earnings for a player compared to what was planned. Thus, we look at the possibilities to implement live tests to quantum random number generators, and propose such tests. Our study has covered six commonly available tools for random number testing, and we show that in particular one of these stands out in that it has a series of tests that fail our quantum random number generator as not random enough, despite passing an pseudo random number generator. This implies that the quantum random number generator behave differently from the pseudo random number ones, and that we need to think carefully about how we test, what we expect from an random sequence and what we want to use it for.Statistisk slumptalstestning är ett väl studerat ämne som fokuserar på så kallade pseudoslumpgeneatorer, det vill säga algorithmer som producerar slump-liknande sekvenser med tal. Sådana generatorer tenderar att ha vissa defekter, som har exploaterats genom rigorös tesning. Sådan testning har lett till framsteg och idag är pseudoslumpgeneratorer både otroligt snabba och producerar till synes slumpade tal. Framsteg inom kvantfysiken har lett till utvecklingen av kvantslumpgeneratorer, som producerar vad som hävdas vara äkta slump. Självklart vill forskare utvärdera sådan slump, och har då vänt sig till de gamla testerna som utvecklats för pseudoslumpgeneratorer. Den här uppsatsen söker utvärdera hurvida allmänt tillgängliga slumptester är nog bra för att utvärdera kvantslumpgeneratorer. Vi jämför även kvantslumpsekvenser med pseudoslumpsekvenser för att se om dessa väsentligen skiljer sig från varandra och på vilket sätt. Ett annat potentiellt problem med kvantslumpgeneratorer är möjligheten att dessa går sönder under drift. Om till exempel en kvantslumpgenerator används för att slumpgenerera resultatet hos en enarmad bandit kan ett fel göra så att maskinen ger dubbel vinst för en spelare jämfört med planerat. Därmed ser vi över möjligheten att implementera live-tester i kvantslumpgeneratorer, och föreslår några sådana tester. Vår studie har täckt sex allmänt tillgängliga verktyg för slumptalstestning, och vi visar att i synnerhet ett av dessa står ut på så sätt att det har en serie av tester som slumptalen från vår kvantslumpgenerator inte anser är nog slumpade. Trots det visar samma test att sekvensen från pseudoslumpgeneratorerna är bra nog. Detta antyder att kvantslumpgeneratorn beter sig annorlunda mot pseudoslumpgeneratorerna, och att vi behöver tänka över ordentligt kring hur vi testar slumpgeneratorer, vad vi förväntar oss att få ut och hurvida detta påverkar det vi skall använda slumpgeneratorn till

A Code Profiling using Statistical Testing in StART

An exhausted testing is one of the testing strategy that need more time taken due to test the whole test cases in the Software Under Test. Many techniques have been proposed to avoid this situation because the size of the Software Under Test is vary and need to have good testing strategy performance. One of the techniques is Adaptive Random Testing (ART). The ART is one of the enhanced random testing. Due to ART performance is better than pure random testing, it becomes motivation to implement the ART in Aspect Oriented Program (AOP). The ART and random testing are similar in which is selection the first test case with random manner. But, ART add another one characteristic which is the evenness test in domain area. Due to similar for first test case, we proposed a new strategy called StART. In StART, we use statistical testing technique to get the information before we test. This process we named it as code profiling. This code profiling helps in selection first test case in this technique. The result from this phase shows the area that we need to select for test activity

Random walk tests for pseudo-random number generators

It is well known that there are no perfectly good generators of random number sequences, implying the need of testing the randomness of the sequences produced by such generators. There are many tests for measuring the uniformity of random sequences, and here we propose a few new ones, designed by random walks. The experiments we have made show that our tests discover some discrepancies of random sequences passing many other tests