Related papers: Congruence Relations for B\"uchi Automata
This work considers weak deterministic B\"uchi automata reading encodings of non-negative reals in a fixed base. A Real Number Automaton is an automaton which recognizes all encoding of elements of a set of reals. It is explained how to…
We study the links between the topological complexity of an omega context free language and its degree of ambiguity. In particular, using known facts from classical descriptive set theory, we prove that non Borel omega context free…
Symbolic automata are finite state automata that support potentially infinite alphabets, such as the set of rational numbers, generally applied to regular expressions/languages over finite words. In symbolic automata (or automata modulo…
In the present work, we lay out a new theory showing that all automata can always be co-lexicographically partially ordered, and an intrinsic measure of their complexity can be defined and effectively determined, namely, the minimum width…
In this paper we address the question of synchronizing random automata in the critical settings of almost-group automata. Group automata are automata where all letters act as permutations on the set of states, and they are not synchronizing…
An automaton is history-deterministic if its nondeterminism can be resolved on the fly, only using the prefix of the word read so far. This mild form of nondeterminism has attracted particular attention for its applications in synthesis…
The classical algorithm for solving B\"uchi games requires time $O(n\cdot m)$ for game graphs with $n$ states and $m$ edges. For game graphs with constant outdegree, the best known algorithm has running time $O(n^2/\log n)$. We present two…
We introduce the category of dependency automata. A dependency automaton consists of two nondeterministic finite automata, with a relation between their states satisfying conditions. This category is equivalent to deterministic finite…
Saturation is a fundamental game-semantic property satisfied by strategies that interpret higher-order concurrent programs. It states that the strategy must be closed under certain rearrangements of moves, and corresponds to the intuition…
In relational verification, judicious alignment of computational steps facilitates proof of relations between programs using simple relational assertions. Relational Hoare logics (RHL) provide compositional rules that embody various…
An index for a finite automaton is a powerful data structure that supports locating paths labeled with a query pattern, thus solving pattern matching on the underlying regular language. In this paper, we solve the long-standing problem of…
B\"uchi arithmetics BA_n, n >= 2, are extensions of Presburger arithmetic with an unary functional symbol V_n(x) denoting the largest power of n that divides x. Definability of a set in BA_n is equivalent to its recognizability by a finite…
We follow language theoretic approach to synchronizing automata and \v{C}ern\'{y}'s conjecture initiated in a series of recent papers. We find a precise lower bound for the reset complexity of a principal ideal languages. Also we show a…
Traditionally, finite automata theory has been used as a framework for the representation of possibly infinite sets of strings. In this work, we introduce the notion of second-order finite automata, a formalism that combines finite automata…
In this paper, we extensively investigate the new algorithm known as the multi-step BCFW recursion relations. Many interesting mathematical properties are found and understanding these aspects, one can find a systematic way to complete the…
We introduce deterministic suffix-reading automata (DSA), a new automaton model over finite words. Transitions in a DSA are labeled with words. From a state, a DSA triggers an outgoing transition on seeing a word ending with the…
We introduce a method for translating an alternating weak B\"uchi automaton (AWA), which corresponds to a Linear Dynamic Logic (LDL) formula, to an unambiguous B\"uchi automaton (UBA). Our translations generalise constructions for Linear…
Quantum finite automata derive their strength by exploiting interference in complex valued probability amplitudes. Of particular interest is the 2-way model of Ambainis and Watrous that has both quantum and classical states (2QCFA) [A.…
A central question in the theory of automata is which classes of automata can be minimized in polynomial time. We close the remaining gaps for deterministic and history-deterministic automata over infinite words by proving that…
A uniformization of a binary relation is a function that is contained in the relation and has the same domain as the relation. The synthesis problem asks for effective uniformization for classes of relations and functions that can be…