In this work, we describe an adjunction between the comma category of Set-based monads under the V -powerset monad and the category of associative lax extensions of Set-based monads to the category of V -relations. In the process, we give a general construction of the Kleisli extension of a monad to the category of V-relations.

A minimal permutation representation of a finite group G is a faithful G-set with the smallest possible size. We study the structure of such representations and show that for certain groups they may be obtained by a greedy construction. In these situations (except when central involutions intervene) all minimal permutation representations have the same set of orbit sizes. Using the same ideas w...

We present direct subset automata constructions for asynchronous (asyn-chronous cellular, resp.) automata. This provides a solution to the problem of direct determinization for automata with distributed control for languages of nite traces. We use the subset automaton construction and apply Klarlund's progress measure technique in order to complement non-deterministic asynchronous cellular B uc...

The redundancy and the size of networks in large-vocabulary speech recognition systems can have a critical eeect on their overall performance. We describe the use of two new algorithms: weighted determinization and minimization 12]. These algorithms transform recognition labeled networks into equivalent ones that require much less time and space in large-vocabulary speech recognition. They are ...

We examine the determinization of monitors for HML with recursion. We demonstrate that every monitor is equivalent to a deterministic one, which is at most doubly exponential in size with respect to the original monitor. When monitors are described as CCS-like processes, this doubly exponential bound is optimal. When (deterministic) monitors are described as finite automata (as their LTS), then...

In this paperwe adapt thewell-knownBrzozowskideterminizationmethod to fuzzy automata. Thismethod gives better results than all previously knownmethods for determinization of fuzzy automata developed by Bělohlávek [InformSciences 143 (2002)205–209],Li andPedrycz [FuzzySet Syst 156 (2005)68–92], Ignjatović et al. [Inform Sciences 178 (2008) 164–180], and Jančić et al. [Inform Sciences 181 (2011) ...

In this paper we address the synthesis problem for specifications given in linear temporal single-agent epistemic logic, KLTL (or KL1), over single-agent systems having imperfect information of the environment state. [18] have shown that this problem is 2Exptime complete. However, their procedure relies on complex automata constructions that are notoriously resistant to efficient implementation...

We present a uniform construction for converting ω-automata with arbitrary acceptance conditions to equivalent deterministic parity automata (DPW). Given a non-deterministic automaton with n states, our construction gives a DPW with at most 2 2 logn) states and O(n) parity indices. The corresponding bounds when the original automaton is deterministic are O(n!) and O(n), respectively. Our algori...

We present a new disambiguation algorithm for finite automata and functional finite-state transducers. We give a full description of the algorithm, including a detailed pseudocode and analysis, and several illustrating examples. Our algorithm is often more efficient and the result dramatically smaller than the one obtained using determinization for finite automata or an existing disambiguation ...

We introduce a version of operational set theory, OST, without a choice operation, which has a machinery for ∆0 separation based on truth functions and the separation operator, and a new kind of applicative set theory, so-called weak explicit set theory WEST, based on Gödel operations. We show that both the theories and Kripke-Platek set theory KP with infinity are pairwise Π1 equivalent. We al...