arXiv subjects

Angelo Montanari

Publications and source records attributed to Angelo Montanari.

At least 19 recordsLinked to original sources

arXiv2026

The $\Sigma$-Chain Product: A Succinct Model of Automata (De)Composition (Extended Version)

The cascade product is a fundamental construction in automata theory, enabling hierarchical composition of automata and playing a central role in decomposition results such as the Krohn-Rhodes theorem. However, its use is limited by the exponential size required to represent cascades, which stems from the fact that each component may depend on all preceding ones, leading to exponentially large alphabets. To address this issue, we introduce the $\Sigma$-chain product, a restricted variant in which each component depends only on the input alphabet and the component immediately preceding it. We show that $\Sigma$-chains achieve linear-size representations and can be exponentially more succinct than cascades. We prove that $\Sigma$-chains and cascades are expressively equivalent to specific classes of automata, such as permutation-reset automata. As a consequence, we derive that a language is regular if and only if it is recognized by a $\Sigma$-chain of permutation-reset automata. Finally, we analyze structural properties of $\Sigma$-chains of reset automata, including a relation with well-known subclasses of star-free languages.

cs.FL↗

arXiv2026

Fixing FOLIO and MALLS: Verified Annotations and an LLM-assisted Framework to Focus Human Relabeling

Accurate translation from Natural Language to First-Order Logic (NL-to-FOL) underpins neurosymbolic AI systems and Natural Language Inference (NLI), making the quality of NL-to-FOL benchmarks essential---yet these datasets have never been rigorously audited. Our first contribution is to present a systematic human inspection of the validation split of \textsf{FOLIO} and a subset of \textsf{MALLS} test instances, finding that approximately 42.5\% and 42\% of entries, respectively, contain incorrect FOL formalizations (i.e., ground truth labels), with additional rates of ambiguous NL sentences (17.8\% and 51\%) and incorrect NLI labels in \textsf{FOLIO} (8.4\%). Our second contribution is to develop and release corrected ground truths for such datasets, showing that annotation errors distort model evaluation on a reference benchmark task: testing three state-of-the-art LLMs (Gemma~4 31B-it, Qwen3-30B-A3B, and GPT-4o-mini) with the corrected ground truths yields accuracy gains from +11 to +23 percentage points. Motivated by these findings, we propose an LLM-based framework to support humans in manual reviewing NL-to-FOL datasets. By directing reviewers toward the most error-prone instances, we empirically show that it is possible to achieve 90\% dataset accuracy after reviewing fewer than 20\% of instances, compared to over 76\% required by unguided review. We release all human-verified annotations and the code for our framework.

cs.CL↗

arXiv2025

Automata-less Monitoring via Trace-Checking (Extended Version)

In runtime verification, monitoring consists of analyzing the current execution of a system and determining, on the basis of the observed finite trace, whether all its possible continuations satisfy or violate a given specification. This is typically done by synthesizing a monitor--often a Deterministic Finite State Automaton (DFA)--from logical specifications expressed in Linear Temporal Logic (LTL) or in its finite-word variant (LTLf). Unfortunately, the size of the resulting DFA may incur a doubly exponential blow-up in the size of the formula. In this paper, we identify some conditions under which monitoring can be done without constructing such a DFA. We build on the notion of intentionally safe and cosafe formulas, introduced in [Kupferman & Vardi, FMSD, 2001], to show that monitoring of these formulas can be carried out through trace-checking, that is, by directly evaluating them on the current system trace, with a polynomial complexity in the size of both the trace and the formula. In addition, we investigate the complexity of recognizing intentionally safe and cosafe formulas for the safety and cosafety fragments of LTL and LTLf. As for LTLf, we show that all formulas in these fragments are intentionally safe and cosafe, thus removing the need for the check. As for LTL, we prove that the problem is in PSPACE, significantly improving over the EXPSPACE complexity of full LTL.

cs.FL↗

arXiv2025

Do LLMs Really Struggle at NL-FOL Translation? Revealing their Strengths via a Novel Benchmarking Strategy

Due to its expressiveness and unambiguous nature, First-Order Logic (FOL) is a powerful formalism for representing concepts expressed in natural language (NL). This is useful, e.g., for specifying and verifying desired system properties. While translating FOL into human-readable English is relatively straightforward, the inverse problem, converting NL to FOL (NL-FOL translation), has remained a longstanding challenge, for both humans and machines. Although the emergence of Large Language Models (LLMs) promised a breakthrough, recent literature provides contrasting results on their ability to perform NL-FOL translation. In this work, we provide a threefold contribution. First, we critically examine existing datasets and protocols for evaluating NL-FOL translation performance, revealing key limitations that may cause a misrepresentation of LLMs' actual capabilities. Second, to overcome these shortcomings, we propose a novel evaluation protocol explicitly designed to distinguish genuine semantic-level logical understanding from superficial pattern recognition, memorization, and dataset contamination. Third, using this new approach, we show that state-of-the-art, dialogue-oriented LLMs demonstrate strong NL-FOL translation skills and a genuine grasp of sentence-level logic, whereas embedding-centric models perform markedly worse.

cs.AI↗

arXiv2025

Unified Peripartum Database with Natural-Language-to-SQL Capabilities at Udine University Hospital: Design and Prototype

The fragmentation of obstetric information across electronic health record modules, device repositories, and laboratory systems, as it is common in hospitals, hinders both intrapartum care and reproducible research. In this work, we present a practical blueprint for transforming heterogeneous peripartum records into computable, queryable assets by designing and prototyping a unified peripartum relational database with natural-language-to-SQL (NL2SQL) capabilities at the Obstetrics Clinic of Udine University Hospital. Requirements were co-defined with clinicians and formalized as an Entity-Relationship diagram, from which the logical schema and SQL implementation of the database were then derived. The latter integrates heterogeneous sources to connect maternal anamnestic and longitudinal history, current-pregnancy findings, intrapartum course, and delivery and neonatal outcomes. The NL2SQL layer enables clinicians to pose natural-language queries to the system, lowering barriers to audit and exploratory analysis.

cs.DB↗

arXiv2025

Interpretable Early Failure Detection via Machine Learning and Trace Checking-based Monitoring

Monitoring is a runtime verification technique that allows one to check whether an ongoing computation of a system (partial trace) satisfies a given formula. It does not need a complete model of the system, but it typically requires the construction of a deterministic automaton doubly exponential in the size of the formula (in the worst case), which limits its practicality. In this paper, we show that, when considering finite, discrete traces, monitoring of pure past (co)safety fragments of Signal Temporal Logic (STL) can be reduced to trace checking, that is, evaluation of a formula over a trace, that can be performed in time polynomial in the size of the formula and the length of the trace. By exploiting such a result, we develop a GPU-accelerated framework for interpretable early failure detection based on vectorized trace checking, that employs genetic programming to learn temporal properties from historical trace data. The framework shows a 2-10% net improvement in key performance metrics compared to the state-of-the-art methods.

cs.AI↗

arXiv2025

Synthesis of timeline-based planning strategies avoiding determinization

Qualitative timeline-based planning models domains as sets of independent, but interacting, components whose behaviors over time, the timelines, are governed by sets of qualitative temporal constraints (ordering relations), called synchronization rules. Its plan-existence problem has been shown to be PSPACE-complete; in particular, PSPACE-membership has been proved via reduction to the nonemptiness problem for nondeterministic finite automata. However, nondeterministic automata cannot be directly used to synthesize planning strategies as a costly determinization step is needed. In this paper, we identify a fragment of qualitative timeline-based planning whose plan-existence problem can be directly mapped into the nonemptiness problem of deterministic finite automata, which can then synthesize strategies. In addition, we identify a maximal subset of Allen's relations that fits into such a deterministic fragment.

cs.AI↗

arXiv2024

Synthesis of Timeline-Based Planning Strategies Avoiding Determinization

Qualitative timeline-based planning models domains as sets of independent, but interacting, components whose behaviors over time, the timelines, are governed by sets of qualitative temporal constraints (ordering relations), called synchronization rules. Its plan-existence problem has been shown to be PSPACE-complete; in particular, PSPACE-membership has been proved via reduction to the nonemptiness problem for nondeterministic finite automata. However, nondeterministic automata cannot be directly used to synthesize planning strategies as a costly determinization step is needed. In this paper, we identify a large fragment of qualitative timeline-based planning whose plan-existence problem can be directly mapped into the nonemptiness problem of deterministic finite automata, which can then be exploited to synthesize strategies. In addition, we identify a maximal subset of Allen's relations that fits into such a deterministic fragment.

cs.FL↗

arXiv2024

Succinctness of Cosafety Fragments of LTL via Combinatorial Proof Systems (extended version)

This paper focuses on succinctness results for fragments of Linear Temporal Logic with Past (LTL) devoid of binary temporal operators like until, and provides methods to establish them. We prove that there is a family of cosafety languages (Ln)_{n>=1} such that Ln can be expressed with a pure future formula of size O(n), but it requires formulae of size 2^{\Omega}(n) to be captured with past formulae. As a by-product, such a succinctness result shows the optimality of the pastification algorithm proposed in [Artale et al., KR, 2023]. We show that, in the considered case, succinctness cannot be proven by relying on the classical automata-based method introduced in [Markey, Bull. EATCS, 2003]. In place of this method, we devise and apply a combinatorial proof system whose deduction trees represent LTL formulae. The system can be seen as a proof-centric (one-player) view on the games used by Adler and Immerman to study the succinctness of CTL.

cs.LO↗

arXiv2023

Controller Synthesis for Timeline-based Games

In the timeline-based approach to planning, the evolution over time of a set of state variables (the timelines) is governed by a set of temporal constraints. Traditional timeline-based planning systems excel at the integration of planning with execution by handling temporal uncertainty. In order to handle general nondeterminism as well, the concept of timeline-based games has been recently introduced. It has been proved that finding whether a winning strategy exists for such games is 2EXPTIME-complete. However, a concrete approach to synthesize controllers implementing such strategies is missing. This paper fills this gap, by providing an effective and computationally optimal approach to controller synthesis for timeline-based games.

cs.AI↗

arXiv2023

The Logic of Prefixes and Suffixes is Elementary under Homogeneity

In this paper, we study the finite satisfiability problem for the logic BE under the homogeneity assumption. BE is the cornerstone of Halpern and Shoham's interval temporal logic, and features modal operators corresponding to the prefix (a.k.a. "Begins") and suffix (a.k.a. "Ends") relations on intervals. In terms of complexity, BE lies in between the "Chop logic C", whose satisfiability problem is known to be non-elementary, and the PSPACE-complete interval logic D of the sub-interval (a.k.a. "During") relation. BE was shown to be EXPSPACE-hard, and the only known satisfiability procedure is primitive recursive, but not elementary. Our contribution consists of tightening the complexity bounds of the satisfiability problem for BE, by proving it to be EXPSPACE-complete. We do so by devising an equi-satisfiable normal form with boundedly many nested modalities. The normalization technique resembles Scott's quantifier elimination, but it turns out to be much more involved due to the limitations enforced by the homogeneity assumption.

cs.LO↗

arXiv2023

AIOSA: An approach to the automatic identification of obstructive sleep apnea events based on deep learning

Obstructive Sleep Apnea Syndrome (OSAS) is the most common sleep-related breathing disorder. It is caused by an increased upper airway resistance during sleep, which determines episodes of partial or complete interruption of airflow. The detection and treatment of OSAS is particularly important in stroke patients, because the presence of severe OSAS is associated with higher mortality, worse neurological deficits, worse functional outcome after rehabilitation, and a higher likelihood of uncontrolled hypertension. The gold standard test for diagnosing OSAS is polysomnography (PSG). Unfortunately, performing a PSG in an electrically hostile environment, like a stroke unit, on neurologically impaired patients is a difficult task; also, the number of strokes per day outnumbers the availability of polysomnographs and dedicated healthcare professionals. Thus, a simple and automated recognition system to identify OSAS among acute stroke patients, relying on routinely recorded vital signs, is desirable. The majority of the work done so far focuses on data recorded in ideal conditions and highly selected patients, and thus it is hardly exploitable in real-life settings, where it would be of actual use. In this paper, we propose a convolutional deep learning architecture able to reduce the temporal resolution of raw waveform data, like physiological signals, extracting key features that can be used for further processing. We exploit models based on such an architecture to detect OSAS events in stroke unit recordings obtained from the monitoring of unselected patients. Unlike existing approaches, annotations are performed at one-second granularity, allowing physicians to better interpret the model outcome. Results are considered to be satisfactory by the domain experts. Moreover, based on a widely-used benchmark, we show that the proposed approach outperforms current state-of-the-art solutions.

cs.LG↗

arXiv2022

Complexity of Safety and coSafety Fragments of Linear Temporal Logic

Linear Temporal Logic (LTL) is the de-facto standard temporal logic for system specification, whose foundational properties have been studied for over five decades. Safety and cosafety properties define notable fragments of LTL, where a prefix of a trace suffices to establish whether a formula is true or not over that trace. In this paper, we study the complexity of the problems of satisfiability, validity, and realizability over infinite and finite traces for the safety and cosafety fragments of LTL. As for satisfiability and validity over infinite traces, we prove that the majority of the fragments have the same complexity as full LTL, that is, they are PSPACE-complete. The picture is radically different for realizability: we find fragments with the same expressive power whose complexity varies from 2EXPTIME-complete (as full LTL) to EXPTIME-complete. Notably, for all cosafety fragments, the complexity of the three problems does not change passing from infinite to finite traces, while for all safety fragments the complexity of satisfiability (resp., realizability) over finite traces drops to NP-complete (resp., ${\Pi}^P_2$-complete).

cs.LO↗

arXiv2022

Controller Synthesis for Timeline-based Games

In the timeline-based approach to planning, originally born in the space sector, the evolution over time of a set of state variables (the timelines) is governed by a set of temporal constraints. Traditional timeline-based planning systems excel at the integration of planning with execution by handling temporal uncertainty. In order to handle general nondeterminism as well, the concept of timeline-based games has been recently introduced. It has been proved that finding whether a winning strategy exists for such games is 2EXPTIME-complete. However, a concrete approach to synthesize controllers implementing such strategies is missing. This paper fills this gap, outlining an approach to controller synthesis for timeline-based games.

cs.AI↗

arXiv2022

A first-order logic characterization of safety and co-safety languages

Linear Temporal Logic (LTL) is one of the most popular temporal logics, that comes into play in a variety of branches of computer science. Among the various reasons of its widespread use there are its strong foundational properties: LTL is equivalent to counter-free omega-automata, to star-free omega-regular expressions, and (by Kamp's theorem) to the First-Order Theory of Linear Orders (FO-TLO). Safety and co-safety languages, where a finite prefix suffices to establish whether a word does not belong or belongs to the language, respectively, play a crucial role in lowering the complexity of problems like model checking and reactive synthesis for LTL. SafetyLTL (resp., coSafetyLTL) is a fragment of LTL where only universal (resp., existential) temporal modalities are allowed, that recognises safety (resp., co-safety) languages only. The main contribution of this paper is the introduction of a fragment of FO-TLO, called SafetyFO, and of its dual coSafetyFO, which are expressively complete with respect to the LTL-definable safety and co-safety languages. We prove that they exactly characterize SafetyLTL and coSafetyLTL, respectively, a result that joins Kamp's theorem, and provides a clearer view of the characterization of (fragments of) LTL in terms of first-order languages. In addition, it gives a direct, compact, and self-contained proof that any safety language definable in LTL is definable in SafetyLTL as well. As a by-product, we obtain some interesting results on the expressive power of the weak tomorrow operator of SafetyLTL, interpreted over finite and infinite words. Moreover, we prove that, when interpreted over finite words, SafetyLTL (resp. coSafetyLTL) devoid of the tomorrow (resp., weak tomorrow) operator captures the safety (resp., co-safety) fragment of LTL over finite words.

cs.AI↗

arXiv2022

A combined approach to the analysis of speech conversations in a contact center domain

The ever more accurate search for deep analysis in customer data is a really strong technological trend nowadays, quite appealing to both private and public companies. This is particularly true in the contact center domain, where speech analytics is an extremely powerful methodology for gaining insights from unstructured data, coming from customer and human agent conversations. In this work, we describe an experimentation with a speech analytics process for an Italian contact center, that deals with call recordings extracted from inbound or outbound flows. First, we illustrate in detail the development of an in-house speech-to-text solution, based on Kaldi framework, and evaluate its performance (and compare it to Google Cloud Speech API). Then, we evaluate and compare different approaches to the semantic tagging of call transcripts, ranging from classic regular expressions to machine learning models based on ngrams and logistic regression, and propose a combination of them, which is shown to provide a consistent benefit. Finally, a decision tree inducer, called J48S, is applied to the problem of tagging. Such an algorithm is natively capable of exploiting sequential data, such as texts, for classification purposes. The solution is compared with the other approaches and is shown to provide competitive classification performances, while generating highly interpretable models and reducing the complexity of the data preparation phase. The potential operational impact of the whole process is thoroughly examined.

cs.CL↗

arXiv2021

Expressiveness of Extended Bounded Response LTL

Extended Bounded Response LTL with Past (LTLEBR+P) is a safety fragment of Linear Temporal Logic with Past (LTL+P) that has been recently introduced in the context of reactive synthesis. The strength of LTLEBR+P is a fully symbolic compilation of formulas into symbolic deterministic automata. Its syntax is organized in four levels. The first three levels feature (a particular combination of) future temporal modalities, the last one admits only past temporal operators. At the base of such a structuring there are algorithmic motivations: each level corresponds to a step of the algorithm for the automaton construction. The complex syntax of LTLEBR+P made it difficult to precisely characterize its expressive power, and to compare it with other LTL+P safety fragments. In this paper, we first prove that LTLEBR+P is expressively complete with respect to the safety fragment of LTL+P, that is, any safety language definable in LTL+P can be formalized in LTLEBR+P, and vice versa. From this, it follows that LTLEBR+P and Safety-LTL are expressively equivalent. Then, we show that past modalities play an essential role in LTLEBR+P: we prove that the future fragment of LTLEBR+P is strictly less expressive than full LTLEBR+P.

cs.FL↗

arXiv2021

Adding the Relation Meets to the Temporal Logic of Prefixes and Infixes makes it EXPSPACE-Complete

The choice of the right trade-off between expressiveness and complexity is the main issue in interval temporal logic. In their seminal paper, Halpern and Shoham showed that the satisfiability problem for HS (the temporal logic of Allen's relations) is highly undecidable over any reasonable class of linear orders. In order to recover decidability, one can restrict the set of temporal modalities and/or the class of models. In the following, we focus on the satisfiability problem for HS fragments under the homogeneity assumption, according to which any proposition letter holds over an interval if only if it holds at all its points. The problem for full HS with homogeneity has been shown to be non-elementarily decidable, but its only known lower bound is EXPSPACE (in fact, EXPSPACE-hardness has been shown for the logic of prefixes and suffixes BE, which is a very small fragment of it. The logic of prefixes and infixes BD has been recently shown to be PSPACE-complete. In this paper, we prove that the addition of the Allen relation Meets to BD makes it EXPSPACE-complete.

cs.LO↗