On hyperbolicity of SU(2)-equivariant, punctured disc bundles over the complex affine quadric

Given a holomorphic line bundle over the complex affine quadric $Q^2$, we investigate its Stein, SU(2)-equivariant disc bundles. Up to equivariant biholomorphism, these are all contained in a maximal one, say $\Omega_{max}$. By removing the zero section to $\Omega_{max}$ one obtains the unique Stein, SU(2)-equivariant, punctured disc bundle over $Q^2$ which contains entire curves. All other such punctured disc bundles are shown to be Kobayashi hyperbolic.Comment: 15 pages, v2: minor changes, to appear in Transformation Group

A Landscape of First-Order Linear Temporal Logics in Infinite-State Verification and Temporal Ontologies

We provide an overview of the main attempts to formalize and reason about the evolution over time of complex domains, through the lens of first-order temporal logics. Different communities have studied similar problems for decades, and some unification of concepts, problems and formalisms is a much needed but not simple task

Torwards Infinite-State Verification and Planning with Linear Temporal Logic Modulo Theories

In this extended abstract, we discuss about Linear Temporal Logic Modulo Theories over finite traces (LTLMTf ), a temporal logic that we recently introduced with the goal of providing an equilibrium between generality of the formalism and decidability of the logic. After recalling its distinguishing features, we discuss some future applications. 2012 ACM Subject Classification Theory of computation → Logic and verificatio

Decidable Fragments of LTLf Modulo Theories

We study Linear Temporal Logic Modulo Theories over Finite Traces (LTLMTf), a recently introduced extension of LTL over finite traces (LTLf) where propositions are replaced by first-order formulas and where first-order variables referring to different time points can be compared. In general, LTLMTf was shown to be semi-decidable for any decidable first-order theory (e.g., linear arithmetics), with a tableau-based semi-decision procedure. In this paper we present a sound and complete pruning rule for the LTLMTf tableau. We show that for any LTLMTf formula that satisfies an abstract, semantic condition, that we call finite memory, the tableau augmented with the new rule is also guaranteed to terminate. Last but not least, this technique allows us to establish novel decidability results for the satisfiability of several fragments of LTLMTf, as well as to give new decidability proofs for classes that are already known

Qualitative past Timeline-Based Games

This extended abstract discusses timeline-based planning, a modeling approach that offers a unique way to model complex systems. Recently, the timeline-based planning framework has been extended to handle general nondeterminism in a game-theoretic setting, resulting in timeline-based games. In this context, the problem of establishing whether a timeline-based game admits a winning strategy and synthesizing such a strategy have been addressed. We propose exploring simpler yet expressive fragments of timeline-based games by leveraging results about the role of past operators in synthesis from temporal logic specifications. The qualitative fragment of timeline-based planning is a good starting point for this exploration. We suggest introducing syntactic restrictions on synchronization rules so that they only constrain the behavior of the system before the current time point, which is expected to lower the complexity of synthesizing timeline-based games to EXPTIME. 2012 ACM Subject Classification Computing methodologies → Planning for deterministic action

SAT Meets Tableaux for Linear Temporal Logic Satisfiability

Linear temporal logic (LTL) and its variant interpreted on finite traces (LTLf) are among the most popular specification languages in the fields of formal verification, artificial intelligence, and others. In this paper, we focus on the satisfiability problem for LTLand LTLfformulas, for which many techniques have been devised during the last decades. Among these are tableau systems, of which the most recent is Reynolds’ tree-shaped tableau. We provide a SAT-based algorithm for LTLand LTLfsatisfiability checking based on Reynolds’ tableau, proving its correctness and discussing experimental results obtained through its implementation in the BLACK satisfiability checker

BIOMASS EXPLOITATION FOR ENERGY SUPPLY AND QUALITY COMPOST PRODUCTION. AN EXEMPLARY CASE OF CIRCULAR ECONOMY IN THE NORTH EAST OF ITALY

The goal 12 of the 2030 Agenda for Sustainable Development takes into consideration the responsible consumption and production in the perspective of circular economy. The agri-food sector is more actively involved in these initiatives, because it offers the possibility to exploit waste and by-products, by adopting suitable biotechnologies. Such processes can be carried out either under aerobic conditions, for the production of compost, or anaerobically, for the production of biogas. In this work the case of a plant managed by Desag Ecologia, located in the municipality of Sedegliano, in the North-East of Italy, is presented. The plant started up in June 2016. Its main activity consists in exploitation of the organic fraction of municipal solid waste and urban forestry green waste coming from separate waste collection. The basin of provenance of collected materials consists not only of the province of Udine, but also of other areas of the Friuli Venezia Giulia region and other northern Italian regions. The plant ensures the production of both biogas (used in a cogeneration installation for producing electricity and heat) and quality compost, which can be used in agriculture, after submission to physico-chemical analyses to verify the end-of-waste status. In this way, the reduction of waste disposal in landfill is ensured. Thermal energy is partially recovered for the production of hot water to heat the anaerobic digester, the leachate collection tank and the plant rooms. Approximately 10% of electricity is self-consumed for the needs of the anaerobic facility, the remaining amount is fed straight into the public electricity network

A Linear-size Cascade Decomposition for Wheeler Automata

The Krohn-Rhodes Decomposition Theorem (KRDT) is a central result in automata and semigroup theories: it states that any (deterministic) finite-state automaton can be disassembled into a collection of automata of two simple types, that can be arranged into a combination - cascade - that simulates the original automaton. The elementary building blocks of the decomposition are either resets or permutations. The full-fledged theorem features two orthogonal dimensions of complexity: the type and the number of building blocks appearing in the cascade, and a deep step in the proof is the characterization of the permutations appearing in the decomposition. This characterization implies, in the case of counter-free automata, that the resulting cascade contains no permutations. In this paper we start analysing KRDT for two compression-oriented classes of automata: (i) path- coherent: state-ordered automata mapping state-intervals to state-intervals; (ii) Wheeler: a subclass of path-coherent automata whose order is the one induced by the co-lexicographic order of words. These classes were recently defined and studied and they turn out to be efficiently encodable and indexable. We prove that each automata in these classes can be decomposed as a cascade with a number of components which is linear in the number of states of the original automaton and, for the Wheeler class, we prove that only two-state resets are needed. Our line of reasoning avoids the necessity of using full KRDT and proves our results directly by a simple inductive argument

SMT-Based Symbolic Model-Checking for Operator Precedence Languages

Operator Precedence Languages (OPL) have been recently identified as a suitable formalism for model checking recursive procedural programs, thanks to their ability of modeling the program stack. OPL requirements can be expressed in the Precedence Oriented Temporal Logic (POTL), which features modalities to reason on the natural matching between function calls and returns, exceptions, and other advanced programming constructs that previous approaches, such as Visibly Pushdown Languages, cannot model effectively. Existing approaches for model checking of POTL have been designed following the explicit-state, automata-based approach, a feature that severely limits their scalability. In this paper, we give the first symbolic, SMT-based approach for model checking POTL properties. While previous approaches construct the automaton for both the POTL formula and the model of the program, we encode them into a (sequence of) SMT formulas. The search of a trace of the model witnessing a violation of the formula is then carried out by an SMT-solver, in a Bounded Model Checking fashion. We carried out an experimental evaluation, which shows the effectiveness of the proposed solution

On Cascades of Reset Automata

The Krohn-Rhodes decomposition theorem is a pivotal result in automata theory. It introduces the concept of cascade product, where two semiautomata, that is, automata devoid of initial and final states, are combined in a feed-forward fashion. The theorem states that any semiautomaton can be decomposed into a sequence of permutation-reset semiautomata. For the counter-free case, this decomposition consists entirely of reset components with two states each. This decomposition has significantly impacted recent research in various areas of computer science, including the identification of a class of transformer encoders equivalent to star-free languages and the conversion of Linear Temporal Logic formulas into past-only expressions (pastification). The paper revisits the cascade product in the context of reset automata, thus considering each component of the cascade as a language acceptor. First, we give regular expression counterparts of cascades of reset automata. We then establish several expressiveness results, identifying hierarchies of languages based on the restriction of the height (number of components) of the cascade or of the number of states in each level. We also show that any cascade of reset automata can be transformed, with a quadratic increase in height, into a cascade that only includes two-state components. Finally, we show that some fundamental operations on cascades, like intersection, union, negation, and concatenation with a symbol to the left, can be directly and efficiently computed by adding a two-state component