202 research outputs found

    Distinguishing experiments for timed nondeterministic finite state machine

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    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

    Acta Cybernetica : Volume 21. Number 2.

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    The Word Problem for Omega-Terms over the Trotter-Weil Hierarchy

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    For two given ω\omega-terms α\alpha and β\beta, the word problem for ω\omega-terms over a variety V\boldsymbol{\mathrm{V}} asks whether α=β\alpha=\beta in all monoids in V\boldsymbol{\mathrm{V}}. We show that the word problem for ω\omega-terms over each level of the Trotter-Weil Hierarchy is decidable. More precisely, for every fixed variety in the Trotter-Weil Hierarchy, our approach yields an algorithm in nondeterministic logarithmic space (NL). In addition, we provide deterministic polynomial time algorithms which are more efficient than straightforward translations of the NL-algorithms. As an application of our results, we show that separability by the so-called corners of the Trotter-Weil Hierarchy is witnessed by ω\omega-terms (this property is also known as ω\omega-reducibility). In particular, the separation problem for the corners of the Trotter-Weil Hierarchy is decidable

    History-deterministic Parikh Automata

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    Parikh automata extend finite automata by counters that can be tested for membership in a semilinear set, but only at the end of a run. Thereby, they preserve many of the desirable properties of finite automata. Deterministic Parikh automata are strictly weaker than nondeterministic ones, but enjoy better closure and algorithmic properties. This state of affairs motivates the study of intermediate forms of nondeterminism. Here, we investigate history-deterministic Parikh automata, i.e., automata whose nondeterminism can be resolved on the fly. This restricted form of nondeterminism is well-suited for applications which classically call for determinism, e.g., solving games and composition. We show that history-deterministic Parikh automata are strictly more expressive than deterministic ones, incomparable to unambiguous ones, and enjoy almost all of the closure and some of the algorithmic properties of deterministic automata.Comment: arXiv admin note: text overlap with arXiv:2207.0769

    Parikh Automata over Infinite Words

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    Parikh automata extend finite automata by counters that can be tested for membership in a semilinear set, but only at the end of a run, thereby preserving many of the desirable algorithmic properties of finite automata. Here, we study the extension of the classical framework onto infinite inputs: We introduce reachability, safety, B\"uchi, and co-B\"uchi Parikh automata on infinite words and study expressiveness, closure properties, and the complexity of verification problems. We show that almost all classes of automata have pairwise incomparable expressiveness, both in the deterministic and the nondeterministic case; a result that sharply contrasts with the well-known hierarchy in the ω\omega-regular setting. Furthermore, emptiness is shown decidable for Parikh automata with reachability or B\"uchi acceptance, but undecidable for safety and co-B\"uchi acceptance. Most importantly, we show decidability of model checking with specifications given by deterministic Parikh automata with safety or co-B\"uchi acceptance, but also undecidability for all other types of automata. Finally, solving games is undecidable for all types
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