Searcharxiv⌕ Search

arXiv subjects

Florin Manea

Publications and source records attributed to Florin Manea.

At least 19 recordsLinked to original sources
arXiv2026

Tractable Gap-Constraint Languages for Complex Event Recognition

For strings $u, D \in \Sigma^*$, a subsequence embedding of $u$ in $D$ is a function $e \colon \{1, 2, \ldots, |u|\} \to \{1, 2, \ldots, |D|\}$ with $e(i) < e(i+1)$ for every $i \in \{1, 2, \ldots, |u|-1\}$ and the $i$-th symbol of $u$ equals the $e(i)$-th symbol of $D$. A gap-constraint for $u$ is a triple $(i, j, L)$ with $1 \leq i < j \leq |u|$ and $L$ is a regular language over $\Sigma$. An embedding $e$ satisfies a gap-constraint $(i, j, L)$ if the factor of $D$ strictly between positions $e(i)$ and $e(j)$ is a word from $L$. We investigate the subsequence matching problem with gap-constraints, which is relevant in the context of complex event recognition (CER): given $u, D \in \Sigma^*$ and a set $C$ of gap-constraints, find an embedding of $u$ in $D$ that satisfies all gap-constraints from $C$. In general, subsequence matching is NP-complete and the only known tractable variants restrict the interval structure of the gap-constraints. In this work, we show that we can solve subsequence matching with gap-constraints with an arbitrary interval structure rather efficiently (in fact, optimally under SETH) in time $O(|D| (|u| + |C|))$ if the gap-constraint languages satisfy a property which we dub left-convexity: whenever $u v w \in L$ and $v \in L$, then also $uv \in L$. Left-convex languages are sufficiently expressive to model interesting real-world scenarios considered in CER, e.g., length constraints $L = \{w \mid a \leq |w| \leq b\}$ for $a, b \in \mathbb{N}$. We also show how our algorithm can be used in order to efficiently enumerate all satisfying embeddings, which is particularly relevant for possible applications in CER. Finally, we show how non-left-convex languages can lead to intractability, i.e., if in addition to length constraints we allow $\{aa, \epsilon\}$ as the only non-left-convex constraint language, then the problem is NP-complete again.

cs.DS↗
arXiv2025

Entanglement Entropy of a Non-Minimally Coupled Self-Interacting Scalar across a Schwarzschild Horizon at $\mathcal{O}(\alpha)$

We compute the first-order correction in the quartic coupling $\alpha$ to the entanglement entropy of a massive, non-minimally coupled scalar across the horizon of a four-dimensional Schwarzschild black hole, treating the non-minimal coupling $\xi$ as a free parameter. Combining the replica trick on the conical manifold $\mathcal{M}_n$ with heat-kernel methods in proper-time regularization, we obtain a closed-form expression for $\delta S^{(1)}(m,\alpha,\xi)$. The bare correction exhibits a log-enhanced quadratic divergence $\epsilon^{-2}\ln(m^2\epsilon^2)$, arising from interference between bulk fluctuations and the distributional curvature at the tip; we show it is cancelled at $\mathcal{O}(\alpha)$ by the bulk mass counterterm. The residual $m^2\ln(m^2\epsilon^2)$ divergence renormalizes Newton's constant, preserving $S_{\mathrm{BH}} = \mathcal{A}_\Sigma / 4 G_F$. The correction is proportional to $(1/6-\xi)$ and vanishes identically for conformal coupling.

gr-qc↗
arXiv2025

Efficiently Finding All Minimal and Shortest Absent Subsequences in a String

Given a string $w$, another string $v$ is said to be a subsequence of $w$ if $v$ can be obtained from $w$ by removing some of its letters; on the other hand, $v$ is called an absent subsequence of $w$ if $v$ is not a subsequence of $w$. The existing literature on absent subsequences focused on understanding, for a string $w$, the set of its shortest absent subsequences (i.e., the shortest strings which are absent subsequences of $w$) and that of its minimal absent subsequences (i.e., those strings which are absent subsequences of $w$ but whose every proper subsequence occurs in $w$). Our contributions to this area of research are the following. Firstly, we present optimal algorithms (with linear time preprocessing and output-linear delay) for the enumeration of the shortest and, respectively, minimal absent subsequences. Secondly, we present optimal algorithms for the incremental enumeration of these strings with linear time preprocessing and constant delay; in this setting, we only output short edit-scripts showing how the currently enumerated string differs from the previous one. Finally, we provide an efficient algorithm for identifying a longest minimal absent subsequence of a string. All our algorithms improve the state-of-the-art results for the aforementioned problems.

cs.DS↗
arXiv2025

Linear Time Subsequence and Supersequence Regex Matching

It is well-known that checking whether a given string $w$ matches a given regular expression $r$ can be done in quadratic time $O(|w|\cdot |r|)$ and that this cannot be improved to a truly subquadratic running time of $O((|w|\cdot |r|)^{1-\epsilon})$ assuming the strong exponential time hypothesis (SETH). We study the related problem that asks whether $w$ has a \emph{subsequence} that matches $r$, and we show that surprisingly this task admits an algorithm that runs in linear time, i.e., in $O(|w| + |r|)$. We further show that the same holds if we ask for a supersequence instead of a subsequence. Moreover, we show that the \emph{quantitative} problems of computing a longest subsequence or shortest supersequence of $w$ that matches $r$ can be solved with the same complexity as the classical longest common subsequence or shortest common supersequence problems, i.e., in $O(|w|\cdot |r|)$, and conditionally not in $O((|w|\cdot|r|)^{1 - \epsilon})$. By contrast, if instead of subsequences or supersequences we consider other string relations like the infix, prefix, left-extension, or extension relations, then all the corresponding problems (both quantitative and non-quantitative) have the same complexity as classical regex matching, i.e., they can also be solved in $O(|w|\cdot |r|)$, but not in $O((|w|\cdot|r|)^{1 - \epsilon})$ assuming SETH. We last study the complexity of the \emph{universal} problem that asks if \emph{all} subsequences (or supersequences, infixes, prefixes, left-extensions or extensions) of an input string satisfy a given regular expression. For these problems, we show polynomial upper bounds (along with matching conditional lower bounds) for the infix and prefix relations, but PSPACE-completeness for the extension, left-extension and supersequence relations, and coNP-completeness for the subsequence relation.

cs.DS↗
arXiv2025

$k$-Universality of Regular Languages Revisited

A subsequence of a word $w$ is a word $u$ such that $u = w[i_1] w[i_2] \cdots w[i_k]$, for some set of indices $1 \leq i_1 < i_2 < \dots < i_k \leq \vert w \vert$. A word $w$ is \emph{$k$-subsequence universal} over an alphabet $\Sigma$ if every word over $\Sigma$ up to length $k$ appears in $w$ as a subsequence. In this paper, we revisit the problem $k$-ESU of deciding, for a given integer $k$, whether a regular language, given either as nondeterministic finite automaton or as a regular expression, contains a $k$-universal word. [Adamson et al., ISAAC 2023] showed that this problem is NP-hard, even in the case when $k=1$, and an FPT algorithm w.r.t. the size of the input alphabet was given. In this paper, we improve the aforementioned algorithmic result and complete the analysis of this problem w.r.t. other parameters. That is, we propose a more efficient FPT algorithm for $k$-ESU, with respect to the size of the input alphabet, and propose new FPT algorithms for this problem w.r.t.~the number of states of the input automaton and the length of the input regular expression. We also discuss corresponding lower bounds. Our results significantly improve the understanding of this problem.

cs.FL↗
arXiv2024

Subsequence Matching and Analysis Problems for Formal Languages

In this paper, we study a series of algorithmic problems related to the subsequences occurring in the strings of a given language, under the assumption that this language is succinctly represented by a grammar generating it, or an automaton accepting it. In particular, we focus on the following problems: Given a string $w$ and a language $L$, does there exist a word of $L$ which has $w$ as subsequence? Do all words of $L$ have $w$ as a subsequence? Given an integer $k$ alongside $L$, does there exist a word of $L$ which has all strings of length $k$, over the alphabet of $L$, as subsequences? Do all words of $L$ have all strings of length $k$ as subsequences? For the last two problems, efficient algorithms were already presented in [Adamson et al., ISAAC 2023] for the case when $L$ is a regular language, and efficient solutions can be easily obtained for the first two problems. We extend that work as follows: we give sufficient conditions on the class of input-languages, under which these problems are decidable; we provide efficient algorithms for all these problems in the case when the input language is context-free; we show that all problems are undecidable for context-sensitive languages. Finally, we provide a series of initial results related to a class of languages that strictly includes the regular languages and is strictly included in the class of context-sensitive languages, but is incomparable to the of class context-free languages; these results deviate significantly from those reported for language-classes from the Chomsky hierarchy.

cs.FL↗
arXiv2024

Revisiting Weighted Information Extraction: A Simpler and Faster Algorithm for Ranked Enumeration

Information extraction from textual data, where the query is represented by a finite transducer and the task is to enumerate all results without repetition, and its extension to the weighted case, where each output element has a weight and the output elements are to be enumerated sorted by their weights, are important and well studied problems in database theory. On the one hand, the first framework already covers the well-known case of regular document spanners, while the latter setting covers several practically relevant tasks that cannot be described in the unweighted setting. It is known that in the unweighted case this problem can be solved with linear time preprocessing $O(|D|)$ and output-linear delay $O(|s|)$ in data complexity, where $D$ is the input data and $s$ is the current output element. For the weighted case, Bourhis, Grez, Jachiet, and Riveros [ICDT 2021] recently designed an algorithm with linear time preprocessing, but the delay of $O(|s| \cdot \log|\mathsf{D}|)$ depends on the size of the data. We first show how to leverage the existing results on enumerating shortest paths to obtain a simple alternative algorithm with linear preprocessing and a delay of $O(|s_i| + \min\{ \log i, \log|\mathsf{D}|\})$ for the $i^{\text{th}}$ output element $s_i$ (in data complexity); thus, substantially improving the previous algorithm. Next, we develop a technically involved rounding technique that allows us to devise an algorithm with linear time preprocessing and output-linear delay $O(|s|)$ with high probability. To this end, we combine tools from algebra, high-dimensional geometry, and linear programming.

cs.DS↗
arXiv2024

Proceedings 14th International Workshop on Non-Classical Models of Automata and Applications (NCMA 2024)

The Fourteenth International Workshop on Non-Classical Models of Automata and Applications (NCMA 2024) was held in G\"ottingen, Germany, on August 12 and 13, 2024, at the historic Georg-Augustus-Universit\"at, organized by the Theoretical Computer Science research group of the respective university. The NCMA workshop series was established in 2009 as an annual event for researchers working on non-classical and classical models of automata, grammars or related devices. Such models are investigated both as theoretical models and as formal models for applications from various points of view. The goal of the NCMA workshop series is to exchange and develop novel ideas in order to gain deeper and interdisciplinary coverage of this particular area that may foster new insights and substantial progress.

cs.FL↗
arXiv2024

Tight Bounds for the Number of Absent Subsequences

A {\em subsequence} of a word $w$ is a word $u$ that can be obtained by deleting some letters from $w$ while maintaining the relative order of the remaining letters, e.g., $\mathtt{lala}$ is a subsequence of $\mathtt{alfalfa}$. A word, over some alphabet $\Sigma$, which has all possible words of length $\iota$ over $\Sigma$ as subsequences is called $\iota$-universal, and the largest $\iota$ for which this holds is called the universality index of $w$, and denoted $\iota(w)$. Moreover, words that are not subsequences of $w$ are called absent subsequences (AS) of $w$, and their investigation was started in (Kosche et al., 2022). In this paper, we present tight bounds on the number of AS of a given length $k$ among all words with the same universality index $\iota$. For both the lower and upper bound, we construct words that have, respectively, a minimal and maximal number of absent subsequences of the respective length $k$, and, in the case of the lower bound, we provide the exact number of missing subsequences as a closed form. Finally, we present efficient enumeration algorithms for the set of subsequences of given length of a word: we give a novel, optimal enumeration algorithm with output linear delay of this set of subsequences, with preprocessing time $O(|w|)$, which is further improved to an incremental enumeration algorithm with $O(1)$ delay of this set of subsequences, with preprocessing time $O(|w|)$.

cs.FL↗
arXiv2024

Subsequences With Generalised Gap Constraints: Upper and Lower Complexity Bounds

For two strings u, v over some alphabet A, we investigate the problem of embedding u into w as a subsequence under the presence of generalised gap constraints. A generalised gap constraint is a triple (i, j, C_{i, j}), where 1 <= i < j <= |u| and C_{i, j} is a subset of A^*. Embedding u as a subsequence into v such that (i, j, C_{i, j}) is satisfied means that if u[i] and u[j] are mapped to v[k] and v[l], respectively, then the induced gap v[k + 1..l - 1] must be a string from C_{i, j}. This generalises the setting recently investigated in [Day et al., ISAAC 2022], where only gap constraints of the form C_{i, i + 1} are considered, as well as the setting from [Kosche et al., RP 2022], where only gap constraints of the form C_{1, |u|} are considered. We show that subsequence matching under generalised gap constraints is NP-hard, and we complement this general lower bound with a thorough (parameterised) complexity analysis. Moreover, we identify several efficiently solvable subclasses that result from restricting the interval structure induced by the generalised gap constraints.

cs.DS↗
arXiv2024

Layered and Staged Monte Carlo Tree Search for SMT Strategy Synthesis

Modern SMT solvers, such as Z3, offer user-controllable strategies, enabling users to tailor solving strategies for their unique set of instances, thus dramatically enhancing solver performance for their use case. However, this approach of strategy customization presents a significant challenge: handcrafting an optimized strategy for a class of SMT instances remains a complex and demanding task for both solver developers and users alike. In this paper, we address this problem of automatic SMT strategy synthesis via a novel Monte Carlo Tree Search (MCTS) based method. Our method treats strategy synthesis as a sequential decision-making process, whose search tree corresponds to the strategy space, and employs MCTS to navigate this vast search space. The key innovations that enable our method to identify effective strategies, while keeping costs low, are the ideas of layered and staged MCTS search. These novel heuristics allow for a deeper and more efficient exploration of the strategy space, enabling us to synthesize more effective strategies than the default ones in state-of-the-art (SOTA) SMT solvers. We implement our method, dubbed Z3alpha, as part of the Z3 SMT solver. Through extensive evaluations across six important SMT logics, Z3alpha demonstrates superior performance compared to the SOTA synthesis tool FastSMT, the default Z3 solver, and the CVC5 solver on most benchmarks. Remarkably, on a challenging QF_BV benchmark set, Z3alpha solves 42.7% more instances than the default strategy in the Z3 SMT solver.

cs.AI↗
arXiv2024

Enumerating m-Length Walks in Directed Graphs with Constant Delay

In this paper, we provide a novel enumeration algorithm for the set of all walks of a given length within a directed graph. Our algorithm has worst-case constant delay between outputting succinct representations of such walks, after a preprocessing step requiring linear time relative to the size of the graph. We apply these results to the problem of enumerating succinct representations of the strings of a given length from a prefix-closed regular language (languages accepted by a finite automaton which has final states only).

cs.DS↗
arXiv2023

$k$-Universality of Regular Languages

A subsequence of a word $w$ is a word $u$ such that $u = w[i_1] w[i_2] \dots w[i_{k}]$, for some set of indices $1 \leq i_1 < i_2 < \dots < i_k \leq \lvert w\rvert$. A word $w$ is $k$-subsequence universal over an alphabet $\Sigma$ if every word in $\Sigma^k$ appears in $w$ as a subsequence. In this paper, we study the intersection between the set of $k$-subsequence universal words over some alphabet $\Sigma$ and regular languages over $\Sigma$. We call a regular language $L$ \emph{$k$-$\exists$-subsequence universal} if there exists a $k$-subsequence universal word in $L$, and \emph{$k$-$\forall$-subsequence universal} if every word of $L$ is $k$-subsequence universal. We give algorithms solving the problems of deciding if a given regular language, represented by a finite automaton recognising it, is \emph{$k$-$\exists$-subsequence universal} and, respectively, if it is \emph{$k$-$\forall$-subsequence universal}, for a given $k$. The algorithms are FPT w.r.t.~the size of the input alphabet, and their run-time does not depend on $k$; they run in polynomial time in the number $n$ of states of the input automaton when the size of the input alphabet is $O(\log n)$. Moreover, we show that the problem of deciding if a given regular language is \emph{$k$-$\exists$-subsequence universal} is NP-complete, when the language is over a large alphabet. Further, we provide algorithms for counting the number of $k$-subsequence universal words (paths) accepted by a given deterministic (respectively, nondeterministic) finite automaton, and ranking an input word (path) within the set of $k$-subsequence universal words accepted by a given finite automaton.

cs.FL↗
arXiv2023

Sem\"enov Arithmetic, Affine VASS, and String Constraints

We study extensions of Sem\"enov arithmetic, the first-order theory of the structure $(\mathbb{N}, +, 2^x)$. It is well-knonw that this theory becomes undecidable when extended with regular predicates over tuples of number strings, such as the B\"uchi $V_2$-predicate. We therefore restrict ourselves to the existential theory of Sem\"enov arithmetic and show that this theory is decidable in EXPSPACE when extended with arbitrary regular predicates over tuples of number strings. Our approach relies on a reduction to the language emptiness problem for a restricted class of affine vector addition systems with states, which we show decidable in EXPSPACE. As an application of our results, we settle an open problem from the literature and show decidability of a class of string constraints involving length constraints.

cs.LO↗
arXiv2023

Longest Common Subsequence with Gap Constraints

We consider the longest common subsequence problem in the context of subsequences with gap constraints. In particular, following Day et al. 2022, we consider the setting when the distance (i. e., the gap) between two consecutive symbols of the subsequence has to be between a lower and an upper bound (which may depend on the position of those symbols in the subsequence or on the symbols bordering the gap) as well as the case where the entire subsequence is found in a bounded range (defined by a single upper bound), considered by Kosche et al. 2022. In all these cases, we present effcient algorithms for determining the length of the longest common constrained subsequence between two given strings.

cs.DS↗
arXiv2022

A Generic Information Extraction System for String Constraints

String constraint solving, and the underlying theory of word equations, are highly interesting research topics both for practitioners and theoreticians working in the wide area of satisfiability modulo theories. As string constraint solving algorithms, a.k.a. string solvers, gained a more prominent role in the formal analysis of string-heavy programs, especially in connection to symbolic code execution and security protocol verification, we can witness an ever-growing number of benchmarks collecting string solving instances from real-world applications as well as an ever-growing need for more efficient and reliable solvers, especially for the aforementioned real-world instances. Thus, it seems that the string solving area (and the developers, theoreticians, and end-users active in it) could greatly benefit from a better understanding and processing of the existing string solving benchmarks. In this context, we propose SMTQUERY: an SMT-LIB benchmark analysis tool for string constraints. SMTQUERY is implemented in Python 3, and offers a collection of analysis and information extraction tools for a comprehensive data base of string benchmarks (presented in SMT-LIB format), based on an SQL-centred language called QLANG.

cs.LO↗