24 research outputs found
A Linear Logic Based Approach to Timed Petri Nets
1.1 Relationship between Petri net and linear logic Petri nets were first introduced by Petri in his seminal Ph.D. thesis, and both the theory and the applications of his model have flourished in concurrency theory (Reisig & Rozenberg, 1998a; Reisig & Rozenberg, 1998b)
State of B\"uchi Complementation
Complementation of B\"uchi automata has been studied for over five decades
since the formalism was introduced in 1960. Known complementation constructions
can be classified into Ramsey-based, determinization-based, rank-based, and
slice-based approaches. Regarding the performance of these approaches, there
have been several complexity analyses but very few experimental results. What
especially lacks is a comparative experiment on all of the four approaches to
see how they perform in practice. In this paper, we review the four approaches,
propose several optimization heuristics, and perform comparative
experimentation on four representative constructions that are considered the
most efficient in each approach. The experimental results show that (1) the
determinization-based Safra-Piterman construction outperforms the other three
in producing smaller complements and finishing more tasks in the allocated time
and (2) the proposed heuristics substantially improve the Safra-Piterman and
the slice-based constructions.Comment: 28 pages, 4 figures, a preliminary version of this paper appeared in
the Proceedings of the 15th International Conference on Implementation and
Application of Automata (CIAA
VLDL Satisfiability and Model Checking via Tree Automata
We present novel algorithms solving the satisfiability problem and the model
checking problem for Visibly Linear Dynamic Logic (VLDL) in asymptotically
optimal time via a reduction to the emptiness problem for tree automata with
B\"uchi acceptance. Since VLDL allows for the specification of important
properties of recursive systems, this reduction enables the efficient analysis
of such systems.
Furthermore, as the problem of tree automata emptiness is well-studied, this
reduction enables leveraging the mature algorithms and tools for that problem
in order to solve the satisfiability problem and the model checking problem for
VLDL.Comment: 14 page
The Hanoi Omega-Automata Format
We propose a flexible exchange format for ω-automata, as typically used in formal verification, and implement support for it in a range of established tools. Our aim is to simplify the interaction of tools, helping the research community to build upon other people’s work. A key feature of the format is the use of very generic acceptance conditions, specified by Boolean combinations of acceptance primitives, rather than being limited to common cases such as Büchi, Streett, or Rabin. Such flexibility in the choice of acceptance conditions can be exploited in applications, for example in probabilistic model checking, and furthermore encourages the development of acceptance-agnostic tools for automata manipulations. The format allows acceptance conditions that are either state-based or transition-based, and also supports alternating automata
The Complexity of Enriched Mu-Calculi
The fully enriched μ-calculus is the extension of the propositional
μ-calculus with inverse programs, graded modalities, and nominals. While
satisfiability in several expressive fragments of the fully enriched
μ-calculus is known to be decidable and ExpTime-complete, it has recently
been proved that the full calculus is undecidable. In this paper, we study the
fragments of the fully enriched μ-calculus that are obtained by dropping at
least one of the additional constructs. We show that, in all fragments obtained
in this way, satisfiability is decidable and ExpTime-complete. Thus, we
identify a family of decidable logics that are maximal (and incomparable) in
expressive power. Our results are obtained by introducing two new automata
models, showing that their emptiness problems are ExpTime-complete, and then
reducing satisfiability in the relevant logics to these problems. The automata
models we introduce are two-way graded alternating parity automata over
infinite trees (2GAPTs) and fully enriched automata (FEAs) over infinite
forests. The former are a common generalization of two incomparable automata
models from the literature. The latter extend alternating automata in a similar
way as the fully enriched μ-calculus extends the standard μ-calculus.Comment: A preliminary version of this paper appears in the Proceedings of the
33rd International Colloquium on Automata, Languages and Programming (ICALP),
2006. This paper has been selected for a special issue in LMC
Structural Reductions and Stutter Sensitive Properties
Verification of properties expressed as -regular languages such as
LTL can benefit hugely from stutter insensitivity, using a diverse set of
reduction strategies. However properties that are not stutter invariant, for
instance due to the use of the neXt operator of LTL or to some form of counting
in the logic, are not covered by these techniques in general. We propose in
this paper to study a weaker property than stutter insensitivity. In a stutter
insensitive language both adding and removing stutter to a word does not change
its acceptance, any stuttering can be abstracted away; by decomposing this
equivalence relation into two implications we obtain weaker conditions. We
define a shortening insensitive language where any word that stutters less than
a word in the language must also belong to the language. A lengthening
insensitive language has the dual property. A semi-decision procedure is then
introduced to reliably prove shortening insensitive properties or deny
lengthening insensitive properties while working with a \emph{reduction} of a
system. A reduction has the property that it can only shorten runs. Lipton's
transaction reductions or Petri net agglomerations are examples of eligible
structural reduction strategies. We also present an approach that can reason
using a partition of a property language into its stutter insensitive,
shortening insensitive, lengthening insensitive and length sensitive parts to
still use structural reductions even when working with arbitrary properties. An
implementation and experimental evidence is provided showing most non-random
properties sensitive to stutter are actually shortening or lengthening
insensitive.Comment: 24 pages, extended version of FORTE'22 paper "LTL under reductions
with weaker conditions than stutter invariance" arXiv:2111.0334