Related papers: Precedence Automata and Languages
In this work we define formal grammars in terms of free monoidal categories, along with a functor from the category of formal grammars to the category of automata. Generalising from the Booleans to arbitrary semirings, we extend our…
Controlled natural languages (CNLs) are effective languages for knowledge representation and reasoning. They are designed based on certain natural languages with restricted lexicon and grammar. CNLs are unambiguous and simple as opposed to…
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 introduce layered automata, a subclass of alternating parity automata that generalises deterministic automata. Assuming a consistency property, these automata are history deterministic and 0-1 probabilistic. We show that every…
In this paper we give automata-based representation of LTL-FO$^+$ properties. LTL-FO$^+$ is an extension of LTL that includes first-order quantification over bounded variable, thus greatly increasing the expressivity of the language. An…
In this paper, we study First Order Logic (FO) over (unordered) infinite trees and its connection with branching-time temporal logics. More specifically, we provide an automata-theoretic characterisation of FO interpreted over infinite…
The class of Unambiguous Star-Free Regular Languages (UL) was defined by Schutzenberger as the class of languages defined by Unambiguous Polynomials. UL has been variously characterized (over finite words) by logics such as TL[X_a,Y_a],…
Analogous to regular string and tree languages, regular languages of directed acyclic graphs (DAGs) are defined in the literature. Although called regular, those DAG-languages are more powerful and, consequently, standard problems have a…
String languages recognizable in (deterministic) log-space are characterized either by two-way (deterministic) multi-head automata, or following Immerman, by first-order logic with (deterministic) transitive closure. Here we elaborate this…
Language models (LMs) are often expected to generate strings in some formal language; for example, structured data, API calls, or code snippets. Although LMs can be tuned to improve their adherence to formal syntax, this does not guarantee…
Finitary Idealized Concurrent Algol (FICA) is a prototypical programming language combining functional, imperative, and concurrent computation. There exists a fully abstract game model of FICA, which in principle can be used to prove…
A predicate linear temporal logic LTL_{\lambda,=} without quantifiers but with predicate abstraction mechanism and equality is considered. The models of LTL_{\lambda,=} can be naturally seen as the systems of pebbles (flexible constants)…
The theory of finite automata concerns itself with words in a free monoid together with concatenation and without further structure. There are, however, important applications which use alphabets which are structured in some sense. We…
Combining ideas from distributed algorithms and alternating automata, we introduce a new class of finite graph automata that recognize precisely the languages of finite graphs definable in monadic second-order logic. By restricting…
In this paper we study the logical aspects of branching automata, as defined by Lodaya and Weil. We first prove that the class of languages of finite N-free posets recognized by branching automata is closed under complementation. Then we…
The problem if a given configuration of a pushdown automaton (PDA) is bisimilar with some (unspecified) finite-state process is shown to be decidable. The decidability is proven in the framework of first-order grammars, which are given by…
Context-free languages are widely used to describe the syntax of programming languages and natural languages. Usually, we describe a context-free language mathematically with the help of context-free grammar (for generation) or pushdown…
Many different deletion operations are investigated applied to languages accepted by one-way and two-way deterministic reversal-bounded multicounter machines, deterministic pushdown automata, and finite automata. Operations studied include…
Geometric folding processes are ubiquitous in natural systems ranging from protein biochemistry to patterns of insect wings and leaves. In a previous study, a folding operation between strings of formal languages was introduced as a model…
Most natural languages have a predominant or fixed word order. For example in English the word order is usually Subject-Verb-Object. This work attempts to explain this phenomenon as well as other typological findings regarding word order…