Related papers: Towards Nominal Formal Languages
Nominal terms extend first-order terms with binding. They lack some properties of first- and higher-order terms: Terms must be reasoned about in a context of 'freshness assumptions'; it is not always possible to 'choose a fresh variable…
In this short survey we describe recent advances on word equations with non-rational constraints in groups and monoids, highlighting the important role that formal languages play in this area.
Relative monads provide a controlled view of computation. We generalise the monadic metalanguage to a relative setting and give a complete semantics with strong relative monads. Adopting this perspective, we generalise two existing program…
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…
Data trees serve as an abstraction of structured data, such as XML documents. A number of specification formalisms for languages of data trees have been developed, many of them adhering to the paradigm of register automata, which is based…
We consider some questions about formal languages that arise when inverses of letters, words and languages are defined. The reduced representation of a language over the free monoid is its unique equivalent representation in the free group.…
We consider languages defined by signed grammars which are similar to context-free grammars except productions with signs associated to them are allowed. As a consequence, the words generated also have signs. We use the structure of the…
The theory of abstract argumentation frameworks (afs) has, in the main, focused on finite structures, though there are many significant contexts where argumentation can be regarded as a process involving infinite objects. To address this…
Generalizations of linear numeration systems in which the set of natural numbers is recognizable by finite automata are obtained by describing an arbitrary infinite regular language following the lexicographic ordering. For these systems of…
Ten years ago, it was shown that nominal techniques can be used to design coalgebraic data types with variable binding, so that alpha-equivalence classes of infinitary terms are directly endowed with a corecursion principle. We introduce…
We define a notion of randomness for individual and collections of formal languages based on automatic martingales acting on sequences of words from some underlying domain. An automatic martingale bets if the incoming word belongs to the…
Nominal abstract syntax and higher-order abstract syntax provide a means for describing binding structure which is higher-level than traditional techniques. These approaches have spawned two different communities which have developed along…
Regular nested word languages (a.k.a. visibly pushdown languages) strictly extend regular word languages, while preserving their main closure and decidability properties. Previous works have shown that considering languages of 2-nested…
Positive data languages are languages over an infinite alphabet closed under possibly non-injective renamings of data values. Informally, they model properties of data words expressible by assertions about equality, but not inequality, of…
Regular languages -- the languages accepted by deterministic finite automata -- are known to be precisely the languages recognized by finite monoids. This characterization is the origin of algebraic language theory. In this paper, we…
This paper proposes a definition of recognizable transducers over monads and comonads, which bridges two important ongoing efforts in the current research on regularity. The first effort is the study of regular transductions, which extends…
We investigate final coalgebras in nominal sets. This allows us to define types of infinite data with binding for which all constructions automatically respect alpha equivalence. We give applications to the infinitary lambda calculus.
Data words with binders formalize concurrently allocated memory. Most name-binding mechanisms in formal languages, such as the $\lambda$-calculus, adhere to properly nested scoping. In contrast, stateful programming languages with explicit…
Nominal Logic is a version of first-order logic with equality, name-binding, renaming via name-swapping and freshness of names. Contrarily to higher-order logic, bindable names, called atoms, and instantiable variables are considered as…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…