Equivalence checking and intersection of deterministic timed finite state machines

Abstract

There has been a growing interest in defining models of automata enriched with time, such as finite automata extended with clocks (timed automata). In this paper, we study deterministic timed finite state machines (TFSMs), i.e., finite state machines with a single clock, timed guards and timeouts which transduce timed input words into timed output words. We solve the problem of equivalence checking by defining a bisimulation from timed FSMs to untimed ones and vice versa. Moreover, we apply these bisimulation relations to build the intersection of two timed finite state machines by untiming them, intersecting them and transforming back to the timed intersection. It is known that many problems like inclusion and equivalence checking are undecidable for timed automata. Our results show that TFSMs correspond to a decidable subclass of timed automata that admits a restricted form of $$\varepsilon $$ ε -transitions (i.e., timeouts) where most of the relevant problems like equivalence and intersection are decidable.

Accelerating Finite State Machine-Based Testing Using Reinforcement Learning

“…Real-time software systems are examples where the state transition may happen due to a timeout. Such systems can be represented by a tFSMs [31], [32], [33] with a single clock. tFSMs have been used as models in many fields, such as in real-time scheduling and optimisation as well as modelchecking, and there are tools for test-case generation from timed FSMs.…”

“…Approaches for test derivation from tFSMs are investigated in many papers [31], [35], [36], [37]. A tFSM can be complete or partial and flattened into an FSM [33]. Thus, test derivation from a given tFSM, and the generation of related RSs and DSs, can be carried out using traditional FSM-based methods from the flattened FSM [36], [37].…”

“…For tFSMs, scalability is adversely affected by the fact that the process of deriving RSs from complete (or partial) tFSMs involves a step that creates a complete (or partial) FSM with many more states than the corresponding tFSM. Our approach can derive RSs directly from the tFSM models without creating partial (or complete) FSMs [33].…”