UIO Sequences Research Articles

$\mathcal k$-branching uio sequences for partially specified observable non-deterministic fsms

In black-box testing, test sequences may be constructed from systems modelled as deterministic finite-state machines (DFSMs) or, more generally, observable non-deterministic finite state machines (ONFSMs). Test sequences usually contain state identification sequences, with unique input output sequences ( <small>UIOs</small> ) often being used with DFSMs. This paper extends the notion of <small>UIOs</small> to ONFSMs. One challenge is that, as a result of non-determinism, the application of an input sequence can lead to exponentially many expected output sequences. To address this scalability problem, we introduce <inline-formula><tex-math notation="LaTeX">${\mathcal K}$</tex-math></inline-formula> - <small>UIOs</small> : <small>UIOs</small> that lead to at most <inline-formula><tex-math notation="LaTeX">${\mathcal K}$</tex-math></inline-formula> output sequences from states of <inline-formula><tex-math notation="LaTeX">$M$</tex-math></inline-formula> . We show that checking <inline-formula><tex-math notation="LaTeX">${\mathcal K}$</tex-math></inline-formula> - <small>UIO</small> existence is PSPACE-Complete if the problem is suitably bounded; otherwise it is in EXPSPACE and PSPACE-Hard. We provide a massively parallel algorithm for constructing <inline-formula><tex-math notation="LaTeX">${\mathcal K}$</tex-math></inline-formula> - <small>UIOs</small> and the results of experiments on randomly generated and real FSM specifications. The proposed algorithm was able to construct <small>UIOs</small> in cases where the existing <small>UIO</small> generation algorithm could not and was able to construct <small>UIOs</small> from FSMs with 38K states and 400K transitions.

Multiple UIO-based test sequence generation for distributed systems

In developing distributed systems, conformance testing is required to determine whether an implementation under test (IUT) conforms to its specification. With distributed test architectures involving multiple remote testers, testing approaches may become more complicated because of issues known as controllability and observability problems. Based on a finite state machine (FSM) representation of the system’s specification, this paper proposes a new method to generate a test sequence utilizing multiple UIO sequences. The method is essentially guided by the way of minimizing the use of external coordination messages and input/output operations. Experiments are given to evaluate the proposed method.

UIO sequence based checking sequences for distributed test architectures

This study addresses the construction of a preset checking sequence that will not pose controllability (synchronization) and observability (undetectable output shift) problems when applied in distributed test architectures that utilize remote testers. The controllability problem manifests itself when a tester is required to send the current input and because it did not send the previous input nor did it receive the previous output it cannot determine when to send the input. The observability problem manifests itself when a tester is expecting an output in response to either the previous input or the current input and because it is not the one to send the current input, it cannot determine when to start and stop waiting for the output. Based on UIO sequences, a checking sequence construction method is proposed to yield a sequence that is free from controllability and observability problems.

Test case generation of a communication protocol by an adaptive state exploration

State exploration, which is widely used for generation of executable test cases for conformance test of a protocol, often causes state explosion problem. This paper proposes an adaptive state exploration method to overcome the problem for a single module protocol. Since state explosion arises in relation to the predicate, it tries to find out efficiently predicated transitions with priority by emulating the normal and erroneous communication environments closely related to the predicates. A test case generation method using the method is also proposed, which uses an Subdivided Extended Finite State Machine (SEFSM) as a protocol model to reduce semantic loss by modeling and adjusted UIO sequences for the protocol model. The empirical results of the proposed methods show their efficacy.

Testing protocols modeled as FSMs with timing parameters

An optimization method is introduced for generating minimum-length test sequences taking into account timing constraints for FSM models of communication protocols. Due to active timers in many of today's protocols, the number of consecutive self-loops that can be traversed in a given state before a timeout occurs is limited. A test sequence that does not consider timing constraints will likely be unrealizable in a test laboratory, thereby potentially resulting in the incorrect failing of valid implementations (or, vice versa). The solution uses a series of augmentations for a protocol's directed graph representation. The resulting test sequence is proven to be of minimum-length while not exceeding the tolerable limit of consecutive self-loops at each state. Although UIO sequences are used for state verification method, the results also are applicable to test generation that uses distinguishing or characterizing sequences.

Dual-state augmentation for minimizing conformance test costs

This paper discusses the dual-state augmentation method to generate the minimum-length test sequences using the multiple UIO sequences of minimal and nonminimal lengths. In dual-state augmentation, all UIO sequences (minimum-length or not) can be used to minimize the test sequence length. The resulting test sequences are significantly shorter than the test sequences generated by the existing methods which only use the minimum-length UIO sequences. As a case study, the dual-state augmentation technique is applied to a subset of the ISDN Network Layer protocol for supplementary voice services. Significant savings on test sequence length are observed.

Graph Algorithms for Conformance Testing Using the Rural Chinese Postman Tour

This paper presents new results and graph algorithms for the automatic testing of protocols using “unique input/output” (UIO) sequences. UIO sequences can be efficiently employed in checking conformance of protocols to their specifications by using transition testing. The optimization of the test sequence is based on finding the rural Chinese postman tour, of the state transition diagram of a finite state machine (FSM). The process of conformance test generation using a touring algorithm is valid provided that certain connectivity properties of the graph are present. This implies that a weakly connected graph must be constructed. It is possible that this connectivity condition may not be met when multiple UIO sequences are used even if the reset capability and/or the self-loop properties are present. The “weakly connected graph problem” consists of finding an edge-induced subgraph of the FSM which is still weakly connected when multiple UIO sequences are used. The “multiple UIO tour minimization problem” addresses the assignment of edges to UIO sequences for minimizing the degree of the directed UIO graph. This process may not also minimize the length of the tour. The above two problems, left open in previous papers, are solved in this paper. It is proved that by appropriately changing the original assignment graph and using network flow techniques with a new UIO generation process referred to as chaining, efficient solutions can be provided. The theoretical approaches behind the solution to these problems are fully characterized.

An Experience in Conformance Testing of an X.25 Implementation

This report describes the conformance testing of the X.25 PLP software on an intelligent X.25 card (maepXLINK) developed in the MAEP project in Indian Telephone Industries (ITI). The test design makes use of UIO sequences to verify the state of the FSM. There is no concept of a ‘test sequence’; instead, transitions are explored in a random fashion, in an attempt to cover unexplored edges each time. We can cover the most probable transitions, or the most important transitions first. The larger the extent of transitions covered, the better is the fault coverage. The method also allows testing to be continued even after an error is detected, if the IUT can be reset either by a single transition or by a sequence of transitions. The method proposed here was used as a supplementary test method for a formal test based on the Chinese Postman Tour problem.

Synchronizable test sequences based on multiple UIO sequences

A test sequence generation method is proposed for testing the conformance of a protocol implementation to its specification in a remote testing system where both external synchronization and input/output operation costs are taken into consideration. The method consists of a set of transformation rules that constructs a duplexU digraph from a given finite state machine (FSM) representation of a protocol specification; and an algorithm that finds a rural postman tour in the duplexU digraph to generate a synchronizable test sequence utilizing multiple UIO sequences. If the protocol satisfies a specific property, namely, the transitions to be tested and the UIO sequences to be employed form a weakly-connected subgraph of the duplexU digraph, the proposed algorithm yields a minimum-cost test sequence. X.25 DTE and ISO Class 0 transport protocols are shown to possess this property. Otherwise, the algorithm yields a test sequence whose cost is within a bound from the cost of the minimum-cost test sequence. The bound for the test sequence generated from the Q.931 network-side protocol is shown to be the cost sum of an input/output operation pair and an external synchronization operation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Synchronizable test sequence generation using UIO sequences

This study addresses the synchronization problem that arises during the application of a predetermined test sequence in some protocol test architectures that utilize remote testers. This problem can usually be solved by coordinating the actions of the remote testers using a test management protocol, a ferry protocol with inter-process communication, or a telephone/terminal connection. However, these solutions either require an additional communication channel or an additional protocol for coordination between the testers. Such requirements can be eliminated by constructing a synchronizable test sequence such that the corresponding sequence of transitions causes no synchronization problem. A heuristic we develop in this study constructs a synchronizable test sequence from a given strongly biconnected digraph representing a deterministic and minimal FSM using synchronizable UIO sequences for each state of the given FSM.

An optimization technique for protocol conformance test generation based on UIO sequences and rural Chinese postman tours

A method for generating test sequences for checking the conformance of a protocol implementation to its specification is described. A rural Chinese postman tour problem algorithm is used to determine a minimum-cost tour of the transition graph of a finite-state machine. It is shown that, when the unique input/output sequence (UIO) is used in place of the more cumbersome distinguishing sequence, both the controllability and observability problems of the protocol testing problem are addressed, providing an efficient method for computing a test sequence for protocol conformance testing.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Protocol conformance test generation using multiple UIO sequences with overlapping

This paper describes an optimization method for reducing the length of protocol conformance test sequences by overlapping test subsequences obtained using UIO sequences. It is shown that test sequences generated by this method are substantially shorter than those generated by other methods employing UIO sequences.

An improved protocol test generation procedure based on UIOS

This paper shows the Unique Input/Output, UIO, approach and the Distinguishing Sequence, DS, approach for the conformance testing of protocol implementations do not always produce identical fault converges, contrary to a previous claim. In the UIO approach, when UIO sequences and signatures are not unique in an implementation, they may not be able to detect erroneous states in the implementation. The UIO approach is revised here with the addition of a verification procedure to ensure that the UIO sequences are all unique in an implementation. Since signatures are generally not unique, this revision requires substituting the use of a signature for a state, S, with a set of input/output sequences, IO(S,K)s, unique to S, each of which distinguishes S from at least one other state, K. Verification is then applied to the IO(S,K)s. Fault coverage in the revised UIO, UIOv, approach is better than that in the original approach. A uniqueness criterion is discussed here to capture a desirable fault coverage for finite-state machine, FSM, test sequences. This criterion ensures the detection of any faulty FSM implementation provided that its set of states does not exceed that in the specified FSM. It is shown that test sequences generated by the UIOv approach and the DS approach always satisfy the uniqueness criterion. In fact, the DS approach is a special case of the UIOv approach; however, the UIOv approach has wider applicability and is generally applicable to k-distinguishable FSMs.