arXiv subjects

Simon Prucker

Publications and source records attributed to Simon Prucker.

5 recordsLinked to original sources

arXiv2026

Nominal Automata with Name Deallocation

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 memory allocation and deallocation, such as C, commonly interleave the scopes of allocated memory regions. This phenomenon is captured in dedicated formalisms such as dynamic sequences and bracket algebra, which similarly feature explicit allocation and deallocation of letters. One of the classical formalisms for data languages are register automata, which have been shown to be equivalent to automata models over nominal sets. In the present work, we introduce a nominal automaton model for languages of data words with explicit allocation and deallocation that strongly resemble dynamic sequences, extending existing nominal automata models by adding deallocating transitions. Using a finite NFA-type representation of the model, we establish a Kleene theorem that shows equivalence with a natural expression language. Moreover, we show that our non-deterministic model allows for determinization, a quite unusual phenomenon in the realm of nominal and register automata.

cs.FL↗

arXiv2025

Efficient Model Checking for the Alternating-Time {\mu}-Calculus via Effectivity Frames

The semantics of alternating-time temporal logic (ATL) and the more expressive alternating-time {\mu}-calculus (AMC) is standardly given in terms of concurrent game frames (CGF). The information required to interpret AMC formulas is equivalently represented in terms of effectivity frames in the sense of Pauly; in many cases, this representation is more compact than the corresponding CGF, and in principle allows for faster evaluation of coalitional modalities. In the present work, we investigate whether implementing a model checker based on effectivity frames leads to better performance in practice. We implement the translation from concurrent game frames to effectivity frames and analyse performance gains in model checking based on corresponding instantiations of a generic model checker for coalgebraic {\mu}-calculi, using dedicated benchmark series as well as random systems and formulas. In the process, we also compare performance to the state-of-the-art ATL model checkerMCMAS. Our results indicate that on large systems, the overhead involved in converting a CGF to an effectivity frame is often outweighed by the benefits in subsequent model checking.

cs.LO↗

arXiv2024

Nominal Tree Automata With Name Allocation

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 on storing data values encountered on the tree in registers for subsequent comparison with further data values. Already on word languages, the expressiveness of such automata models typically increases with the power of control (e.g. deterministic, non-deterministic, alternating). Language inclusion is typically undecidable for non-deterministic or alternating models unless the number of registers is radically restricted, and even then often remains non-elementary. We present an automaton model for data trees that retains a reasonable level of expressiveness, in particular allows non-determinism and any number of registers, while admitting language inclusion checking in elementary complexity, in fact in parametrized exponential time. We phrase the description of our automaton model in the language of nominal sets, building on the recently introduced paradigm of explicit name allocation in nominal automata.

cs.FL↗

arXiv2023

Generic Model Checking for Modal Fixpoint Logics in COOL-MC

We report on COOL-MC, a model checking tool for fixpoint logics that is parametric in the branching type of models (nondeterministic, game-based, probabilistic etc.) and in the next-step modalities used in formulae. The tool implements generic model checking algorithms developed in coalgebraic logic that are easily adapted to concrete instance logics. Apart from the standard modal $\mu$-calculus, COOL-MC currently supports alternating-time, graded, probabilistic and monotone variants of the $\mu$-calculus, but is also effortlessly extensible with new instance logics. The model checking process is realized by polynomial reductions to parity game solving, or, alternatively, by a local model checking algorithm that directly computes the extensions of formulae in a lazy fashion, thereby potentially avoiding the construction of the full parity game. We evaluate COOL-MC on informative benchmark sets.

cs.LO↗

arXiv2023

COOL 2 -- A Generic Reasoner for Modal Fixpoint Logics

There is a wide range of modal logics whose semantics goes beyond relational structures, and instead involves, e.g., probabilities, multi-player games, weights, or neighbourhood structures. Coalgebraic logic serves as a unifying semantic and algorithmic framework for such logics. It provides uniform reasoning algorithms that are easily instantiated to particular, concretely given logics. The COOL 2 reasoner provides an implementation of such generic algorithms for coalgebraic modal fixpoint logics. As concrete instances, we obtain in particular reasoners for the aconjunctive and alternation-free fragments of the graded $\mu$-calculus and the alternating-time $\mu$-calculus. We evaluate the tool on standard benchmark sets for fixpoint-free graded modal logic and alternating-time temporal logic (ATL), as well as on a dedicated set of benchmarks for the graded $\mu$-calculus.

cs.LO↗