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Formal languages over infinite alphabets serve as abstractions of structures and processes carrying data. Automata models over infinite alphabets, such as classical register automata or, equivalently, nominal orbit-finite automata, tend to…
We realize constant-space quantum computation by measure-many two-way quantum finite automata and evaluate their language recognition power by analyzing patterns of their exotic behaviors and by exploring their structural properties. In…
We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…
The problem of computing the edit-distance between a string and a finite automaton arises in a variety of applications in computational biology, text processing, and speech recognition. This paper presents linear-space algorithms for…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
Numerous computer systems use dynamic control and data structures of unbounded size. These data structures have often the character of trees or they can be encoded as trees with some additional pointers. This is exploited by some currently…
Nominal set plays a central role in a group-theoretic extension of finite automata to those over an infinite set of data values. Moerman et al. proposed an active learning algorithm for nominal word automata with the equality symmetry. In…
We first propose algorithms for checking language equivalence of finite automata over a large alphabet. We use symbolic automata, where the transition function is compactly represented using a (multi-terminal) binary decision diagrams…
Automata over infinite words, also known as omega-automata, play a key role in the verification and synthesis of reactive systems. The spectrum of omega-automata is defined by two characteristics: the acceptance condition (e.g. B\"uchi or…
Weighted automata (WA) are an important formalism to describe quantitative properties. Obtaining equivalent deterministic machines is a longstanding research problem. In this paper we consider WA with a set semantics, meaning that the…
Weighted timed automata have been defined in the early 2000's for modelling resource-consumption or -allocation problems in real-time systems. Optimal reachability is decidable in weighted timed automata, and a symbolic forward algorithm…
Orbit-finite sets are a generalisation of finite sets, and as such support many operations allowed for finite sets, such as pairing, quotienting, or taking subsets. However, they do not support function spaces, i.e. if X and Y are…
Classic grammars and regular expressions can be used for a variety of purposes, including parsing, intent detection, and matching. However, the comparisons are performed at a structural level, with constituent elements (words or characters)…
We consider decision problems for relations over finite and infinite words defined by finite automata. We prove that the equivalence problem for binary deterministic rational relations over infinite words is undecidable in contrast to the…
We define guarded variable automata (GVAs), a simple extension of finite automata over infinite alphabets. In this model the transitions are labelled by letters or variables ranging over an infinite alphabet and guarded by conjunction of…
Complexity classes such as $\#\mathbf{P}$, $\oplus\mathbf{P}$, $\mathbf{GapP}$, $\mathbf{OptP}$, $\mathbf{NPMV}$, or the class of fuzzy languages realised by polynomial-time fuzzy nondeterministic Turing machines, can all be described in…
Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the…
In a recent paper we analyzed the space complexity of streaming algorithms whose goal is to decide membership of a sliding window to a fixed language. For the class of regular languages we proved a space trichotomy theorem: for every…
Algorithms which learn environments represented by automata in the past have had complexity scaling with the number of states in the automaton, which can be exponentially large even for automata recognizing regular expressions with a small…
We show how to efficiently enumerate a class of finite-memory stochastic processes using the causal representation of epsilon-machines. We characterize epsilon-machines in the language of automata theory and adapt a recent algorithm for…