Related papers: Monadic Second-Order Logic with Arbitrary Monadic …
$\omega$-clones are multi-sorted structures that naturally emerge as algebras for infinite trees, just as $\omega$-semigroups are convenient algebras for infinite words. In the algebraic theory of languages, one hopes that a language is…
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…
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…
We define a new class of languages of $\omega$-words, strictly extending $\omega$-regular languages. One way to present this new class is by a type of regular expressions. The new expressions are an extension of $\omega$-regular expressions…
We develop a general framework for the specification and implementation of systems whose executions are words, or partial orders, over an infinite alphabet. As a model of an implementation, we introduce class register automata, a one-way…
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…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
We introduce an extension of first-order logic that comes equipped with additional predicates for reasoning about an abstract state. Sequents in the logic comprise a main formula together with pre- and postconditions in the style of Hoare…
One of the most interesting questions concerning hierarchical control of discrete-event systems with partial observations is a condition under which the language observability is preserved between the original and the abstracted plant.…
Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been…
Finite 1-safe Petri nets, also called \emph{net systems}, are natural models of asynchronous concurrency. The event structure of a net system describes all its possible executions and their concurrent nature: two events may be causally…
We study a model of one-way quantum automaton where only measurement operations are allowed ($\mon$). We give an algebraic characterization of $\lmo(\Sigma)$, showing that the syntactic monoids of the languages in $\lmo(\Sigma)$ are exactly…
We consider a language together with the subword relation, the cover relation, and regular predicates. For such structures, we consider the extension of first-order logic by threshold- and modulo-counting quantifiers. Depending on the…
The class of Boolean combinations of tree languages recognized by deterministic top-down tree automata (also known as deterministic root-to-frontier automata) is studied. The problem of determining for a given regular tree language whether…
Whether it be in normal form games, or in fair allocations, or in voter preferences in voting systems, a certain pattern of reasoning is common. From a particular profile, an agent or a group of agents may have an incentive to shift to a…
Human beings possess the most sophisticated computational machinery in the known universe. We can understand language of rich descriptive power, and communicate in the same environment with astonishing clarity. Two of the many contributors…
We give a new characterization of the class of rational string functions from formal language theory using order-preserving interpretations with respect to a very weak monadic programming language. This refines the known characterization of…
An important theorem in classical complexity theory is that LOGLOGSPACE=REG, i.e. that languages decidable with double-logarithmic space bound are regular. We consider a transfinite analogue of this theorem. To this end, we introduce…
Regular transductions over finite words have linear input-to-output growth. This class of transductions enjoys many characterizations. Recently, regular transductions have been extended by Boja\'nczyk to polyregular transductions, which…
We study the classification problems over string data for hypotheses specified by formulas of monadic second-order logic MSO. The goal is to design learning algorithms that run in time polynomial in the size of the training set,…