Topic
Undecidable problem
About: Undecidable problem is a research topic. Over the lifetime, 3135 publications have been published within this topic receiving 71238 citations.
Papers published on a yearly basis
Papers
More filters
23 Mar 2000
TL;DR: It is shown that the existence of a Zeno run is Σ11 -complete for semi-linear hybrid automata; it is too complex to be expressed in first-order arithmetic.
Abstract: We define a new class of hybrid automata for which reachability is decidable--a proper superclass of the initialized rectangular hybrid automata--by taking parallel compositions of simple components. Attempting to generalize, we encounter timed automata with algebraic constants. We show that reachability is undecidable for these algebraic timed automata by simulating two-counter Minsky machines. Modifying the construction to apply to parametric timed automata, we reprove the undecidability of the emptiness problem, and then distinguish the dense and discrete-time cases with a new result. The algorithmic complexity-- both classical and parametric--of one-clock parametric timed automata is also examined. We finish with a table of computability-theoretic complexity results, including that the existence of a Zeno run is Σ11 -complete for semi-linear hybrid automata; it is too complex to be expressed in first-order arithmetic.
103 citations
TL;DR: It is proved that checking the existence of a function which, given the n observations corresponding to a behavior ρ ∈ L, decides whether ρ is in K or not is undecidable, which is used to show undecidability of a decentralized supervisory control problem in the discrete event system framework.
101 citations
11 Oct 2011
TL;DR: It follows from Krob's results that the universality problem is decidable for weighted automata with weights in N ∪ {∞}, and that the equality problem is undecidable when the weights are in N €∞.
Abstract: Weighted automata map input words to numerical values. Applications of weighted automata include formal verification of quantitative properties, as well as text, speech, and image processing.
In the 90's, Krob studied the decidability of problems on rational series, which strongly relate to weighted automata. In particular, it follows from Krob's results that the universality problem (that is, deciding whether the values of all words are below some threshold) is decidable for weighted automata with weights in N ∪ {∞}, and that the equality problem is undecidable when the weights are in N ∪ {∞}.
In this paper we continue the study of the borders of decidability in weighted automata, describe alternative and direct proofs of the above results, and tighten them further. Unlike the proofs of Krob, which are algebraic in their nature, our proofs stay in the terrain of state machines, and the reduction is from the halting problem of a two-counter machine. This enables us to significantly simplify Krob's reasoning and strengthen the results to apply already to a very simple class of automata: all the states are accepting, there are no initial nor final weights, and all the weights are from the set {-1, 0, 1}. The fact we work directly with automata enables us to tighten also the decidability results and to show that the universality problem for weighted automata with weights in N ∪ {∞}, and in fact even with weights in Q≥0 ∪ {∞}, is PSPACE-complete. Our results thus draw a sharper picture about the decidability of decision problems for weighted automata, in both the front of equality vs. universality and the front of the N ∪ {∞} vs. the Z ∪ {∞} domains.
101 citations
TL;DR: It is shown that subsumption in the terminological logic of NikL is undecidable and thus that there are no complete algorithms for subsumption or classification in NIKL.
101 citations
TL;DR: The reachability problem for cryptographic protocols represented as processes relying on perfect cryptographic functions is studied and it is shown that the problem is undecidable in general and in PTIME for a subclass of iterated processes that do not rely on pairing.
100 citations