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Florin Manea

Publications and source records attributed to Florin Manea.

At least 37 records · Page 2Linked to original sources
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↗
arXiv2022

Matching Patterns with Variables Under Edit Distance

A pattern $α$ is a string of variables and terminal letters. We say that $α$ matches a word $w$, consisting only of terminal letters, if $w$ can be obtained by replacing the variables of $α$ by terminal words. The matching problem, i.e., deciding whether a given pattern matches a given word, was heavily investigated: it is NP-complete in general, but can be solved efficiently for classes of patterns with restricted structure. If we are interested in what is the minimum Hamming distance between $w$ and any word $u$ obtained by replacing the variables of $α$ by terminal words (so matching under Hamming distance), one can devise efficient algorithms and matching conditional lower bounds for the class of regular patterns (in which no variable occurs twice), as well as for classes of patterns where we allow unbounded repetitions of variables, but restrict the structure of the pattern, i.e., the way the occurrences of different variables can be interleaved. Moreover, under Hamming distance, if a variable occurs more than once and its occurrences can be interleaved arbitrarily with those of other variables, even if each of these occurs just once, the matching problem is intractable. In this paper, we consider the problem of matching patterns with variables under edit distance. We still obtain efficient algorithms and matching conditional lower bounds for the class of regular patterns, but show that the problem becomes, in this case, intractable already for unary patterns, consisting of repeated occurrences of a single variable interleaved with terminals.

cs.DS↗
arXiv2022

Subsequences With Gap Constraints: Complexity Bounds for Matching and Analysis Problems

We consider subsequences with gap constraints, i.e., length-k subsequences p that can be embedded into a string w such that the induced gaps (i.e., the factors of w between the positions to which p is mapped to) satisfy given gap constraints $gc = (C_1, C_2, ..., C_{k-1})$; we call p a gc-subsequence of w. In the case where the gap constraints gc are defined by lower and upper length bounds $C_i = (L^-_i, L^+_i) \in \mathbb{N}^2$ and/or regular languages $C_i \in REG$, we prove tight (conditional on the orthogonal vectors (OV) hypothesis) complexity bounds for checking whether a given p is a gc-subsequence of a string w. We also consider the whole set of all gc-subsequences of a string, and investigate the complexity of the universality, equivalence and containment problems for these sets of gc-subsequences.

cs.CC↗
arXiv2022

Formal Languages via Theories over Strings

We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly pushdown, and deterministic context-free languages. In total, we consider 20 distinct theories and decidability questions for problems such as emptiness and universality for formal languages over them. First, we discuss their relative expressive power and observe a rough division into two hierarchies based on whether or not word equations are present. Second, we consider the decidability status of several important decision problems, such as emptiness and universality. Note that the emptiness problem is equivalent to the satisfiability problem over the corresponding theory. Third, we consider the problem of whether a language in one theory is expressible in another and show several negative results in which this problem is undecidable. These results are particularly relevant in the context of normal forms in both practical and theoretical aspects of string solving.

cs.FL↗
arXiv2021

Matching Patterns with Variables under Hamming Distance

A pattern $α$ is a string of variables and terminal letters. We say that $α$ matches a word $w$, consisting only of terminal letters, if $w$ can be obtained by replacing the variables of $α$ by terminal words. The matching problem, i.e., deciding whether a given pattern matches a given word, was heavily investigated: it is NP-complete in general, but can be solved efficiently for classes of patterns with restricted structure. In this paper, we approach this problem in a generalized setting, by considering approximate pattern matching under Hamming distance. More precisely, we are interested in what is the minimum Hamming distance between $w$ and any word $u$ obtained by replacing the variables of $α$ by terminal words. Firstly, we address the class of regular patterns (in which no variable occurs twice) and propose efficient algorithms for this problem, as well as matching conditional lower bounds. We show that the problem can still be solved efficiently if we allow repeated variables, but restrict the way the different variables can be interleaved according to a locality parameter. However, as soon as we allow a variable to occur more than once and its occurrences can be interleaved arbitrarily with those of other variables, even if none of them occurs more than once, the problem becomes intractable.

cs.DS↗
arXiv2021

String Theories involving Regular Membership Predicates: From Practice to Theory and Back

Widespread use of string solvers in formal analysis of string-heavy programs has led to a growing demand for more efficient and reliable techniques which can be applied in this context, especially for real-world cases. Designing an algorithm for the (generally undecidable) satisfiability problem for systems of string constraints requires a thorough understanding of the structure of constraints present in the targeted cases. In this paper, we investigate benchmarks presented in the literature containing regular expression membership predicates, extract different first order logic theories, and prove their decidability, resp. undecidability. Notably, the most common theories in real-world benchmarks are PSPACE-complete and directly lead to the implementation of a more efficient algorithm to solving string constraints.

cs.CL↗
arXiv2021

An SMT Solver for Regular Expressions and Linear Arithmetic over String Length

We present a novel length-aware solving algorithm for the quantifier-free first-order theory over regex membership predicate and linear arithmetic over string length. We implement and evaluate this algorithm and related heuristics in the Z3 theorem prover. A crucial insight that underpins our algorithm is that real-world instances contain a wealth of information about upper and lower bounds on lengths of strings under constraints, and such information can be used very effectively to simplify operations on automata representing regular expressions. Additionally, we present a number of novel general heuristics, such as the prefix/suffix method, that can be used in conjunction with a variety of regex solving algorithms, making them more efficient. We showcase the power of our algorithm and heuristics via an extensive empirical evaluation over a large and diverse benchmark of 57256 regex-heavy instances, almost 75% of which are derived from industrial applications or contributed by other solver developers. Our solver outperforms five other state-of-the-art string solvers, namely, CVC4, OSTRICH, Z3seq, Z3str3, and Z3-Trau, over this benchmark, in particular achieving a 2.4x speedup over CVC4, 4.4x speedup over Z3seq, 6.4x speedup over Z3-Trau, 9.1x speedup over Z3str3, and 13x speedup over OSTRICH.

cs.LO↗
arXiv2021

Efficiently Testing Simon's Congruence

Simon's congruence $\sim_k$ is defined as follows: two words are $\sim_k$-equivalent if they have the same set of subsequences of length at most $k$. We propose an algorithm which computes, given two words $s$ and $t$, the largest $k$ for which $s\sim_k t$. Our algorithm runs in linear time $O(|s|+|t|)$ when the input words are over the integer alphabet $\{1,\ldots,|s|+|t|\}$ (or other alphabets which can be sorted in linear time). This approach leads to an optimal algorithm in the case of general alphabets as well. Our results are based on a novel combinatorial approach and a series of efficient data structures.

cs.FL↗
arXiv2020

Blocksequences of k-local Words

The locality of words is a relatively young structural complexity measure, introduced by Day et al. in 2017 in order to define classes of patterns with variables which can be matched in polynomial time. The main tool used to compute the locality of a word is called marking sequence: an ordering of the distinct letters occurring in the respective order. Once a marking sequence is defined, the letters of the word are marked in steps: in the ith marking step, all occurrences of the ith letter of the marking sequence are marked. As such, after each marking step, the word can be seen as a sequence of blocks of marked letters separated by blocks of non-marked letters. By keeping track of the evolution of the marked blocks of the word through the marking defined by a marking sequence, one defines the blocksequence of the respective marking sequence. We first show that the words sharing the same blocksequence are only loosely connected, so we consider the stronger notion of extended blocksequence, which stores additional information on the form of each single marked block. In this context, we present a series of combinatorial results for words sharing the extended blocksequence.

cs.FL↗
arXiv2020

The Edit Distance to $k$-Subsequence Universality

A word $u$ is a subsequence of another word $w$ if $u$ can be obtained from $w$ by deleting some of its letters. The word $w$ with alph$(w)=Σ$ is called $k$-subsequence universal if the set of subsequences of length $k$ of $w$ contains all possible words of length $k$ over $Σ$. We propose a series of efficient algorithms computing the minimal number of edit operations (insertion, deletion, substitution) one needs to apply to a given word in order to reach the set of $k$-subsequence universal words.

cs.DS↗
arXiv2020

Reconstructing Words from Right-Bounded-Block Words

A reconstruction problem of words from scattered factors asks for the minimal information, like multisets of scattered factors of a given length or the number of occurrences of scattered factors from a given set, necessary to uniquely determine a word. We show that a word $w \in \{a, b\}^{*}$ can be reconstructed from the number of occurrences of at most $\min(|w|_a, |w|_b)+ 1$ scattered factors of the form $a^{i} b$. Moreover, we generalize the result to alphabets of the form $\{1,\ldots,q\}$ by showing that at most $ \sum^{q-1}_{i=1} |w|_i (q-i+1)$ scattered factors suffices to reconstruct $w$. Both results improve on the upper bounds known so far. Complexity time bounds on reconstruction algorithms are also considered here.

cs.FL↗
arXiv2020

Scattered Factor-Universality of Words

A word $u=u_1\dots u_n$ is a scattered factor of a word $w$ if $u$ can be obtained from $w$ by deleting some of its letters: there exist the (potentially empty) words $v_0,v_1,..,v_n$ such that $w = v_0u_1v_1...u_nv_n$. The set of all scattered factors up to length $k$ of a word is called its full $k$-spectrum. Firstly, we show an algorithm deciding whether the $k$-spectra for given $k$ of two words are equal or not, running in optimal time. Secondly, we consider a notion of scattered-factors universality: the word $w$, with $\letters(w)=Σ$, is called $k$-universal if its $k$-spectrum includes all words of length $k$ over the alphabet $Σ$; we extend this notion to $k$-circular universality. After a series of preliminary combinatorial results, we present an algorithm computing, for a given $k'$-universal word $w$ the minimal $i$ such that $w^i$ is $k$-universal for some $k>k'$. Several other connected problems~are~also~considered.

cs.FL↗
arXiv2019

Fast and Longest Rollercoasters

For $k\geq 3$, a k-rollercoaster is a sequence of numbers whose every maximal contiguous subsequence, that is increasing or decreasing, has length at least $k$; $3$-rollercoasters are called simply rollercoasters. Given a sequence of distinct numbers, we are interested in computing its maximum-length (not necessarily contiguous) subsequence that is a $k$-rollercoaster. Biedl et al. [ICALP 2018] have shown that each sequence of $n$ distinct real numbers contains a rollercoaster of length at least $\lceil n/2\rceil$ for $n>7$, and that a longest rollercoaster contained in such a sequence can be computed in $O(n\log n)$-time. They have also shown that every sequence of $n\geq (k-1)^2+1$ distinct real numbers contains a $k$-rollercoaster of length at least $\frac{n}{2(k-1)}-\frac{3k}{2}$, and gave an $O(nk\log n)$-time algorithm computing a longest $k$-rollercoaster in a sequence of length $n$. In this paper, we give an $O(nk^2)$-time algorithm computing the length of a longest $k$-rollercoaster contained in a sequence of $n$ distinct real numbers; hence, for constant $k$, our algorithm computes the length of a longest $k$-rollercoaster in optimal linear time. The algorithm can be easily adapted to output the respective $k$-rollercoaster. In particular, this improves the results of Biedl et al. [ICALP 2018], by showing that a longest rollercoaster can be computed in optimal linear time. We also present an algorithm computing the length of a longest $k$-rollercoaster in $O(n \log^2 n)$-time, that is, subquadratic even for large values of $k\leq n$. Again, the rollercoaster can be easily retrieved. Finally, we show an $Ω(n \log k)$ lower bound for the number of comparisons in any comparison-based algorithm computing the length of a longest $k$-rollercoaster.

cs.DS↗
arXiv2019

Matching Patterns with Variables

A pattern p (i.e., a string of variables and terminals) matches a word w, if w can be obtained by uniformly replacing the variables of p by terminal words. The respective matching problem, i.e., deciding whether or not a given pattern matches a given word, is generally NP-complete, but can be solved in polynomial-time for classes of patterns with restricted structure. In this paper we overview a series of recent results related to efficient matching for patterns with variables, as well as a series of extensions of this problem.

cs.DS↗
arXiv2019

On Solving Word Equations Using SAT

We present Woorpje, a string solver for bounded word equations (i.e., equations where the length of each variable is upper bounded by a given integer). Our algorithm works by reformulating the satisfiability of bounded word equations as a reachability problem for nondeterministic finite automata, and then carefully encoding this as a propositional satisfiability problem, which we then solve using the well-known Glucose SAT-solver. This approach has the advantage of allowing for the natural inclusion of additional linear length constraints. Our solver obtains reliable and competitive results and, remarkably, discovered several cases where state-of-the-art solvers exhibit a faulty behaviour.

cs.FL↗
arXiv2019

On Modelling the Avoidability of Patterns as CSP

Solving avoidability problems in the area of string combinatorics often requires, in an initial step, the construction, via a computer program, of a very long word that does not contain any word that matches a given pattern. It is well known that this is a computationally hard task. Despite being rather straightforward that, ultimately, all such tasks can be formalized as constraints satisfaction problems, no unified approach to solving them was proposed so far, and very diverse ad-hoc methods were used. We aim to fill this gap: we show how several relevant avoidability problems can be modelled, and consequently solved, in an uniform way as constraint satisfaction problems, using the framework of MiniZinc. The main advantage of this approach is that one is now required only to formulate the avoidability problem in the MiniZinc language, and then the actual search for a solution does not have to be implemented ad-hoc, being instead carried out by a standard CSP-solver.

cs.FL↗