Finite state automata discard software#

The slicing could be done in parallel for separate execution traces. We illustrate the inputs, intermediate key/value pairs, and outputs for k-tails MR in column (c) in Figure 21.3. The reduce function produces one finite-state machine for a group of subtraces by invoking an instance of the k-tails algorithm. MapReduce collects the subtraces belonging to the same group. The map function slices each trace into a set of subtraces on the basis of the group membership of each event. In this chapter we consider one such notion: a group of events is composed of invocations of methods appearing in the same class. Many notions of relatedness may be defined (see ). Many studies propose methods to split the traces and learn a finite-state machine for each subtrace, whose ideas can be instantiated in MapReduce with our general algorithm, and we name it k-tails MR.Д¬onsider the mapping function EVENTSв†’GROUP, where EVENTS is the set of events (i.e., method calls) in the execution traces, and GROUP is a group identifier. However, this finite-state machine may be too large and difficult to comprehend. The algorithms investigate a set of execution traces and produce a single finite-state machine. Many finite-state machine mining algorithms are variants of the k-tails algorithm.

Finite state automata discard software#

Aditya Budi, in The Art and Science of Analyzing Software Data, 2015 21.3.2.3 Finite-state machine mining with MapReduce For example, is a 2-arc transition starting from s1 to be monitored for the sequential arc coverage. Figure 9.9 shows an FSM example and the arc sequences starting from s 1 for calculating the sequential arc coverage. It also identifies the fundamental cyclic sequences in various lengths.

The metric measures the coverage on the basis of an increased sequential depth of state visitation or arc traversal. Therefore, the third class of FSM coverage, called sequential arc coverage ( a.k.a. Even if 100% state and arc coverages are achieved, there is no guarantee that the FSM is bug-free. The arc coverage records the state transitions that are traversed during simulation. The state coverage reports the states that are visited and their frequencies during simulation. As its name implies, this metric is tied to the HDL structure of finite state machines in a design and can be divided into three sub-classes. The FSM coverage plays an important role in verifying the control unit of a design. Input-Output Labeled Transition System (IOLTSs) ( Fernandez et al., 1996) and I/O automata ( Lynch and Tuttle, 1987) are useful extensions of LTSs and automata, respectively, that allow for explicit modeling of discrete input and output actions. Labeled transition systems (LTSs) ( Uselton and Smolka, 1994) are variants of FSMs that remove the finiteness assumption and also relax the tight coupling between input and output (e.g., a sequence of several inputs may lead to a single output in an LTS while in FSMs inputs and outputs are paired). In an FSM the history of interactions with the system (e.g., the current valuations of variables or signals) is represented by the system state and the transitions capture the system output as the result of providing an input to the system. Extensions of such models with variables and data, e.g., extended FSMs and class FSMs, were also proposed for software testing ( Hierons et al., 2009 Hong, 1995).

We further establish a direct connection between space-bounded quantum computation with quantum advice and quantum finite automata whose transitions are dictated by superpositions of transition tables.Finite state machines (FSMs) or finite automata have been used traditionally in hardware modeling and hardware testing ( Lee, 1996). For two-way quantum finite automata equipped with flexible garbage tapes, we show a close relationship between the state complexity of the nonuniform family of such polynomial-size quantum finite automata and the parameterized complexity class induced by logarithmic-space quantum computation assisted by polynomial-size advice. We first present general inclusion and separation relationships among state complexity classes of nonuniform families of various one-way finite automata, including deterministic, nondeterministic, probabilistic, and quantum finite automata having polynomially many inner states. In a similar fashion, we introduce state complexity classes using nonuniform families of quantum finite automata empowered by the flexible use of garbage tapes. Sakoda and Sipser were concerned with nonuniform families of finite automata and they discussed the behaviors of the nonuniform complexity classes defined by such families of finite automata having polynomial-size state complexity. The state complexity of a finite(-state) automaton intuitively measures the size of the description of the automaton.