Finite state verifiers with constant randomness

We give a new characterization of $\mathsf{NL}$ as the class of languages whose members have certificates that can be verified with small error in polynomial time by finite state machines that use a constant number of random bits, as opposed to its conventional description in terms of deterministic logarithmic-space verifiers. It turns out that allowing two-way interaction with the prover does not change the class of verifiable languages, and that no polynomially bounded amount of randomness is useful for constant-memory computers when used as language recognizers, or public-coin verifiers. A corollary of our main result is that the class of outcome problems corresponding to O(log n)-space bounded games of incomplete information where the universal player is allowed a constant number of moves equals NL.Comment: 17 pages. An improved versio

Mutation testing from probabilistic finite state machines

Mutation testing traditionally involves mutating a program in order to produce a set of mutants and using these mutants in order to either estimate the effectiveness of a test suite or to drive test generation. Recently, however, this approach has been applied to specifications such as those written as finite state machines. This paper extends mutation testing to finite state machine models in which transitions have associated probabilities. The paper describes several ways of mutating a probabilistic finite state machine (PFSM) and shows how test sequences that distinguish between a PFSM and its mutants can be generated. Testing then involves applying each test sequence multiple times, observing the resultant output sequences and using results from statistical sampling theory in order to compare the observed frequency of each output sequence with that expected

The complexity of asynchronous model based testing

This is the post-print version of the final paper published in Theoretical Computer Science. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2012 Elsevier B.V.In model based testing (MBT), testing is based on a model MM that typically is expressed using a state-based language such as an input output transition system (IOTS). Most approaches to MBT assume that communications between the system under test (SUT) and its environment are synchronous. However, many systems interact with their environment through asynchronous channels and the presence of such channels changes the nature of testing. In this paper we investigate the situation in which the SUT interacts with its environment through asynchronous channels and the problems of producing test cases to reach a state, execute a transition, or to distinguish two states. In addition, we investigate the Oracle Problem. All four problems are explored for both FIFO and non-FIFO channels. It is known that the Oracle Problem can be solved in polynomial time for FIFO channels but we also show that the three test case generation problems can also be solved in polynomial time in the case where the IOTS is observable but the general test generation problems are EXPTIME-hard. For non-FIFO channels we prove that all of the test case generation problems are EXPTIME-hard and the Oracle Problem in NP-hard, even if we restrict attention to deterministic IOTSs

Pseudorandomness for Approximate Counting and Sampling

We study computational procedures that use both randomness and nondeterminism. The goal of this paper is to derandomize such procedures under the weakest possible assumptions. Our main technical contribution allows one to “boost” a given hardness assumption: We show that if there is a problem in EXP that cannot be computed by poly-size nondeterministic circuits then there is one which cannot be computed by poly-size circuits that make non-adaptive NP oracle queries. This in particular shows that the various assumptions used over the last few years by several authors to derandomize Arthur-Merlin games (i.e., show AM = NP) are in fact all equivalent. We also define two new primitives that we regard as the natural pseudorandom objects associated with approximate counting and sampling of NP-witnesses. We use the “boosting” theorem and hashing techniques to construct these primitives using an assumption that is no stronger than that used to derandomize AM. We observe that Cai's proof that S_2^P ⊆ PP⊆(NP) and the learning algorithm of Bshouty et al. can be seen as reductions to sampling that are not probabilistic. As a consequence they can be derandomized under an assumption which is weaker than the assumption that was previously known to suffice

Testing from a stochastic timed system with a fault model

In this paper we present a method for testing a system against a non-deterministic stochastic finite state machine. As usual, we assume that the functional behaviour of the system under test (SUT) is deterministic but we allow the timing to be non-deterministic. We extend the state counting method of deriving tests, adapting it to the presence of temporal requirements represented by means of random variables. The notion of conformance is introduced using an implementation relation considering temporal aspects and the limitations imposed by a black-box framework. We propose an algorithm for generating a test suite that determines the conformance of a deterministic SUT with respect to a non-deterministic specification. We show how previous work on testing from stochastic systems can be encoded into the framework presented in this paper as an instantiation of our parameterized implementation relation. In this setting, we use a notion of conformance up to a given confidence level

Controllable testing from nondeterministic finite state machines with multiple ports

Copyright @ 2011 IEEESome systems have physically distributed interfaces, called ports, at which they interact with their environment. We place a tester at each port and if the testers cannot directly communicate and there is no global clock then we are using the distributed test architecture. It is known that this test architecture introduces controllability problems when testing from a deterministic finite state machine. This paper investigates the problem of testing from a nondeterministic finite state machine in the distributed test architecture and explores controllability. It shows how we can decide in polynomial time whether an input sequence is controllable. It also gives an algorithm for generating such an input sequence bar{x} and shows how we can produce testers that implement bar{x}

Distinguishing experiments for timed nondeterministic finite state machine

The problem of constructing distinguishing experiments is a fundamental problem in the area of finite state machines (FSMs), especially for FSM-based testing. In this paper, the problem is studied for timed nondeterministic FSMs (TFSMs) with output delays. Given two TFSMs, we derive the TFSM intersection of these machines and show that the machines can be distinguished using an appropriate (untimed) FSM abstraction of the TFSM intersection. The FSM abstraction is derived by constructing appropriate partitions for the input and output time domains of the TFSM intersection. Using the obtained abstraction, a traditional FSM-based preset algorithm can be used for deriving a separating sequence for the given TFSMs if these machines are separable. Moreover, as sometimes two non-separable TFSMs can still be distinguished by an adaptive experiment, based on the FSM abstraction we present an algorithm for deriving an r-distinguishing TFSM that represents a corresponding adaptive experiment