202 research outputs found
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
The Word Problem for Omega-Terms over the Trotter-Weil Hierarchy
For two given -terms and , the word problem for
-terms over a variety asks whether
in all monoids in . We show that the
word problem for -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
-terms (this property is also known as -reducibility). In
particular, the separation problem for the corners of the Trotter-Weil
Hierarchy is decidable
History-deterministic Parikh Automata
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
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
-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
- …