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Temporal Specifications with Accumulative Values
TLDR
This work shows that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities by prefix-accumulation assertions and extending LTL with path-accUMulation assertions, result in temporal logics whose model-checking problem is decidable.
Discounting in LTL
TLDR
One direction in this effort is to refine the “eventually” operators of temporal logic to discounting operators: the satisfaction value of a specification is a value in [0,1], where the longer it takes to fulfill eventuality requirements, the smaller the satisfactionvalue is.
Exact and Approximate Determinization of Discounted-Sum Automata
TLDR
Positive news is provided, showing that every NDA with an integral discount factor is determinizable, and it is proved that the integers characterize exactly the discount factors that guarantee determinizability: for every nonintegral rational discount factor $\lambda$, there is a nondeterminizable $\lambda$-NDA.
What's Decidable about Weighted Automata?
TLDR
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 €∞.
Formally Reasoning About Quality
TLDR
Two quantitative extensions of Linear Temporal Logic are introduced, one by propositional quality operators and one by discounting operators, and the usefulness of both extensions is demonstrated and the decidability and complexity of the decision and search problems for them are studied.
Families of DFAs as Acceptors of omega-Regular Languages
TLDR
It is shown that FDFAs are more succinct than deterministic parity automata (DPAs) in the sense that translating a DPA to an FDFA can always be done with only a polynomial increase, yet the other direction involves an inevitable exponential blowup in the worst case.
The Church-Turing Thesis over Arbitrary Domains
TLDR
It is shown that the Church-Turing Thesis is not well defined for arbitrary domains, and an axiomatization of an "effective model of computation" over an arbitrary countable domain is proposed, based on Gurevich's postulates for sequential algorithms.
Nondeterminism in the Presence of a Diverse or Unknown Future
TLDR
It is shown that GFT=GFG⊃DBP, and described a determinization construction for GFG automata, which shows the possible succinctness of GFG and GFT automata compared to deterministic automata.
Families of DFAs as Acceptors of $ω$-Regular Languages
TLDR
It is shown that FDFAs are more succinct than deterministic parity automata (DPAs) in the sense that translating a DPA to an FDFA can always be done with only a polynomial increase, yet the other direction involves an inevitable exponential blowup in the worst case.
Formalizing and Reasoning about Quality
TLDR
By extending the automata-theoretic approach for LTL to a setting that takes quality into an account, it is able to solve the above problems and show that reasoning about LTL has roughly the same complexity as reasoning about traditional LTL.
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