Related papers: Algebraic Characterization of FO-definable Languag…
In this paper we study finite higher-dimensional automata (HDAs) from the logical point of view. Languages of HDAs are sets of finite bounded-width interval pomsets with interfaces (iiPoms<=k) closed under order extension. We prove that…
We report some further developments regarding the language theory of higher-dimensional automata (HDAs). Regular languages of HDAs are sets of finite interval partially ordered multisets (pomsets) with interfaces. We show a pumping lemma…
We introduce languages of higher-dimensional automata (HDAs) and develop some of their properties. To this end, we define a new category of precubical sets, uniquely naturally isomorphic to the standard one, and introduce a notion of event…
Higher-dimensional automata (HDA) are a formalism to faithfully model the behaviour of concurrent systems. For ordinary automata, there is a correspondence between regular expressions, regular languages and finite automata, which provides a…
In this paper we explore languages of higher-dimensional automata (HDAs) from an algebraic and logical point of view. Such languages are sets of finite width-bounded interval pomsets with interfaces (ipomsets) closed under order extension.…
Temporal logics are a powerful tool to specify properties of computational systems. For concurrent programs, Higher Dimensional Automata (HDA) are a very expressive model of non-interleaving concurrency. HDA recognize languages of partially…
We establish a Myhill-Nerode type theorem for higher-dimensional automata (HDAs), stating that a language is regular if and only if it has finite prefix quotient. HDAs extend standard automata with additional structure, making it possible…
Higher dimensional automata (HDAs) provide a geometric model of true concurrency, yet their standard formulation encodes an artificial total order on events. This representational artifact causes a fundamental mismatch between the…
Higher dimensional automata (HDA) are a model of concurrency that can express most of the traditional partial order models like Mazurkiewicz traces, pomsets, event structures, or Petri nets. Modal logics, interpreted over Kripke structures,…
We present a new language semantics for real-time concurrency. Its operational models are higher-dimensional timed automata (HDTAs), a generalization of both higher-dimensional automata and timed automata. In real-time concurrent systems,…
We introduce higher-dimensional automata for infinite interval ipomsets ($\omega$-HDAs). We define key concepts from different points of view, inspired from their finite counterparts. Then we explore languages recognized by $\omega$-HDAs…
We prove a Kleene theorem for higher-dimensional automata. It states that the languages they recognise are precisely the rational subsumption-closed sets of finite interval pomsets. The rational operations on these languages include a…
The theory of higher-dimensional automata (HDAs) has seen rapid progress in recent years, and first applications, notably to Petri net analysis, are starting to show. It has, however, emerged that HDAs themselves often are too strict a…
Rational word languages can be defined by several equivalent means: finite state automata, rational expressions, finite congruences, or monadic second-order (MSO) logic. The robust subclass of aperiodic languages is defined by: counter-free…
Since the 1970s with the work of McNaughton, Papert and Sch\"utzenberger, a regular language is known to be definable in the first-order logic if and only if its syntactic monoid is aperiodic. This algebraic characterisation of a…
We study the expressiveness and succinctness of history-deterministic pushdown automata (HD-PDA) over finite words, that is, pushdown automata whose nondeterminism can be resolved based on the run constructed so far, but independently of…
We show that for any $i > 0$, it is decidable, given a regular language, whether it is expressible in the $\Sigma_i[<]$ fragment of first-order logic FO[<]. This settles a question open since 1971. Our main technical result relies on the…
Higher-dimensional automata (HDAs) are models of non-interleaving concurrency for analyzing concurrent systems. There is a rich literature that deals with bisimulations for concurrent systems, and some of them have been extended to HDAs.…
The states of a deterministic finite automaton A can be identified with collections of words in Pf(L(A)) -- the set of prefixes of words belonging to the regular language accepted by A. But words can be ordered and among the many possible…
By fundamental results of Sch\"utzenberger, McNaughton and Papert from the 1970s, the classes of first-order definable and aperiodic languages coincide. Here, we extend this equivalence to a quantitative setting. For this, weighted automata…