Abstract Syntactic obligations are a fragment of LTL formulas that translate to deterministic weak $$\omega $$ ω -automata (DWA). We show that syntactic obligations can be very efficiently converted to minimal DWA represented using multi-terminal binary decision diagrams (MTBDDs), and that synthesis of such specifications can be solved directly on the MTBDD representation on the fly. Our implementation in Spot shows substantial runtime improvements in translation and synthesis.

LTLf synthesis under partial observability requires reasoning about unobservable environment variables, which is typically handled by constructing a belief-state DFA via subset construction that universally quantifies these variables. Existing approaches perform this construction as a separate step prior to game solving, often generating belief states that are unnecessary in practice. We propose an on-the-fly approach to LTLf synthesis under partial observability based on observable progression. Our method incrementally builds the belief-state DFA by progressing the specification with respect to observable variables only, universally quantifying unobservable variables on the fly. We prove the correctness of the construction and show that it naturally enables on-the-fly game solving, leading to a fully on-the-fly synthesis framework. Our implementation leverages DFAs represented using Multi-Terminal Binary Decision Diagrams: a compact representation that has proven highly effective for LTLf synthesis under full observability. Experimental results demonstrate that our approach significantly outperforms existing methods and further highlight the practical benefits of integrating on-the-fly game solving with belief-state construction.

Abstract Spot is a C++17 library for LTL and $$\omega $$ ω -automata manipulation, with command-line utilities, and Python bindings. This paper summarizes its evolution over the past six years, since the release of Spot 2.0, which was the first version to support $$\omega $$ ω -automata with arbitrary acceptance conditions, and the last version presented at a conference. Since then, Spot has been extended with several features such as acceptance transformations, alternating automata, games, LTL synthesis, and more. We also shed some lights on the data-structure used to store automata. Artifact: https://zenodo.org/record/6521395 .

Abstract In 2021, Casares, Colcombet, and Fijalkow introduced the Alternating Cycle Decomposition (ACD) to study properties and transformations of Muller automata. We present the first practical implementation of the ACD in two different tools, Owl and Spot, and adapt it to the framework of Emerson-Lei automata, i.e., $$\omega $$ ω -automata whose acceptance conditions are defined by Boolean formulas. The ACD provides a transformation of Emerson-Lei automata into parity automata with strong optimality guarantees: the resulting parity automaton is minimal among those automata that can be obtained by duplication of states. Our empirical results show that this transformation is usable in practice. Further, we show how the ACD can generalize many other specialized constructions such as deciding typeness of automata and degeneralization of generalized Büchi automata, providing a framework of practical algorithms for $$\omega $$ ω -automata.

We present the second generation of the tool Seminator that transforms transition-based generalized Büchi automata (TGBAs) into equivalent semi-deterministic automata. The tool has been extended with numerous optimizations and produces considerably smaller automata than its first version. In connection with the state-of-the-art LTL to TGBAs translator Spot, Seminator 2 produces smaller (on average) semi-deterministic automata than the direct LTL to semi-deterministic automata translator ltl2ldgba of the Owl library. Further, Seminator 2 has been extended with an improved NCSB complementation procedure for semi-deterministic automata, providing a new way to complement automata that is competitive with state-of-the-art complementation tools.

In the automata theoretic approach to explicit state LTL model checking, the synchronized product of the model and an automaton that represents the negated formula is checked for emptiness. In practice, a (transition-based generalized) Büchi automaton (TGBA) is used for this procedure. This paper investigates whether using a more general form of acceptance, namely a transition-based generalized Rabin automaton (TGRA), improves the model checking procedure. TGRAs can have significantly fewer states than TGBAs; however, the corresponding emptiness checking procedure is more involved. With recent advances in probabilistic model checking and LTL to TGRA translators, it is only natural to ask whether checking a TGRA directly is more advantageous in practice. We designed a multi-core TGRA checking algorithm and performed experiments on a subset of the models and formulas from the 2015 Model Checking Contest and generated LTL formulas for models from the BEEM database. While we found little to no improvement by checking TGRAs directly, we show how various aspects of a TGRA’s structure influences the model checking performance. In this paper, we also introduce a Fin-less acceptance condition, which is a disjunction of TGBAs. We show how to convert TGRAs into automata with Fin-less acceptance and show how a TGBA emptiness procedure can be extended to check Fin-less automata.

We present a tool that transforms nondeterministic ω-automata to semi-deterministic ω-automata. The tool Seminator accepts transition-based generalized Bu ̈chi automata (TGBA) as an input and produces automata with two kinds of semi-determinism. The implemented procedure performs degeneralization and semi-determinization simultaneously and employs several other optimizations. We experimentally evaluate Seminator in the context of LTL to semi-deterministic automata translation.

In the automata theoretic approach to explicit state LTL model checking, the synchronized product of the model and an automaton that represents the negated formula is checked for emptiness. In practice, a (transition-based generalized) Büchi automaton (TGBA) is used for this procedure.

LTL to Büchi automata (BA) translators are traditionally optimized to produce automata with a small number of states or a small number of non-deterministic states. In this paper, we search for properties of Büchi automata that really influence the performance of explicit model checkers. We do that by manual analysis of several automata and by experiments with common LTL-to-BA translators and realistic verification tasks. As a result of these experiences, we gain a better insight into the characteristics of automata that work well with Spin.

In this paper we propose a novel approach for color image segmentation. Our approach is based on segmentation of subsets of bands using mathematical morphology followed by the fusion of the resulting segmentation "channels". For color images the band subsets are chosen as RG, RB and GB pairs, whose 2D histograms are processed as projections of a 3D histogram. The segmentations in 2D color spaces are obtained using the watershed algorithm. These 2D segmentations are then combined to obtain a final result using a region split-and-merge process. The CIE L*a*b* color space is used to measure the color distance. Our approach results in improved performance and can be generalized for multiband segmentation of images such as multispectral satellite images.

Algorithm libraries dedicated to image processing and pattern recognition are not reusable; to run an algorithm on particular data, one usually has either to rewrite the algorithm or to manually "copy, paste, and modify". This is due to the lack of genericity of the programming paradigm used to implement the libraries. In this paper, we present a recent paradigm that allows algorithms to be written once and for all and to accept input of various types. Moreover, this total reusability can be obtained with a very comprehensive writing and without significant cost at execution, compared to a dedicated algorithm. This new paradigm is called generic programming and is fully supported by the C++ language. We show how this paradigm can be applied to image processing and pattern recognition routines. The perspective of our work is the creation of a generic library.