76 Search Results for "Lohrey, Markus"

Document
DOI: 10.4230/LIPIcs.LICS.2026.47
Constructing Small Monadic Decompositions in Presburger Arithmetic

Authors: Moses Ganardi and Marin Ricros

Published in: LIPIcs, Volume 380, 41st Annual Symposium on Logic in Computer Science (LICS 2026)

Abstract
A monadic decomposition of a formula over a first-order theory is an equivalent Boolean combination of atomic formulas, each containing only one variable. Monadic decomposition is a generic simplification technique that has found applications in various settings such as quantifier elimination, string solving, and constraint databases. Previous work has mostly focused on the decision problem of whether a formula admits a monadic decomposition. However, much less is known on how to efficiently produce a small monadic decomposition, which is required for any application. We study this question for the quantifier-free fragment of Presburger arithmetic. Here, monadic decomposability is known to be coNP-complete, and monadic decompositions can be computed in exponential time. An exponential size lower bound was only known for monadic decompositions in disjunctive or conjunctive normal form (DNF or CNF). In this work, we extend this exponential lower bound to general monadic decompositions. Guided by this lower bound, we present fragments that admit polynomially-sized monadic decompositions, which, in many cases, can be constructed efficiently. A surprising key ingredient in our proof is a family of small-depth circuits for arithmetic operations in Chinese remainder representation.
Cite as

Moses Ganardi and Marin Ricros. Constructing Small Monadic Decompositions in Presburger Arithmetic. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 47:1-47:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ganardi_et_al:LIPIcs.LICS.2026.47,
  author =	{Ganardi, Moses and Ricros, Marin},
  title =	{{Constructing Small Monadic Decompositions in Presburger Arithmetic}},
  booktitle =	{41st Annual Symposium on Logic in Computer Science (LICS 2026)},
  pages =	{47:1--47:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-434-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{380},
  editor =	{Faggian, Claudia and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.LICS.2026.47},
  URN =		{urn:nbn:de:0030-drops-268346},
  doi =		{10.4230/LIPIcs.LICS.2026.47},
  annote =	{Keywords: Monadic decomposition, variable independence, Presburger arithmetic}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2026.170
Transducers on Compressed Strings

Authors: Mikołaj Bojańczyk and Markus Lohrey

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
We study string-to-string functions which are compatible with compression in the following sense: given a compressed representation of an input string, one can compute in polynomial time a compressed representation of the output string. As the compression formalism, we use straight-line programs (i.e. context-free grammars that produce only one string). As the functions, we use finite state transducers, with a focus on the regular and polyregular functions. We show that all regular functions are compatible with compression, but this is no longer true for the polyregular functions. We identify a subclass of the polyregular functions - the so-called rectangular polyregular functions - which is compatible with compression, and we characterise this subclass in terms of a functional programming language.
Cite as

Mikołaj Bojańczyk and Markus Lohrey. Transducers on Compressed Strings. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 170:1-170:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bojanczyk_et_al:LIPIcs.ICALP.2026.170,
  author =	{Boja\'{n}czyk, Miko{\l}aj and Lohrey, Markus},
  title =	{{Transducers on Compressed Strings}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{170:1--170:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.170},
  URN =		{urn:nbn:de:0030-drops-265580},
  doi =		{10.4230/LIPIcs.ICALP.2026.170},
  annote =	{Keywords: polyregular functions, grammar compression}
}
Document
DOI: 10.4230/LIPIcs.SEA.2026.10
Compressing Highly Repetitive Binary Trees with an Application to Range Minimum Queries

Authors: Gabriel Carmona and Filippo Lari

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract
Tree compression is a well-studied area that aims at reducing the size of tree representations by exploiting different forms of repetition. While the underlying theory is well understood, there is still significant room for experimental investigation, particularly in the design of compressed representations that efficiently support navigational queries. In this work, we address the problem of designing, engineering, and experimentally evaluating a compression technique for unlabeled binary trees based on repeated subtrees, yielding the minimal Directed Acyclic Graph (DAG) of the input tree. We show how this representation can be computed in linear time and space directly from a succinct encoding of the tree, and how it can be augmented with compact auxiliary data structures to support Lowest Common Ancestor (LCA) queries. When the input tree is the Cartesian tree of an array, LCA queries can be used to answer Range Minimum Queries (RMQs) on the underlying array. This is particularly relevant in the encoding model, where the array is not accessible at query time, and a space lower bound of 2n-O(log n) bits is known. Given the numerous applications of RMQs, we use this problem as a case study for our experimental evaluation, testing our implementation on 11 real-world datasets. Our experiments show that, on almost every dataset, our implementation is the most space-efficient, using as few as 0.11n bits, while still delivering practical query times.
Cite as

Gabriel Carmona and Filippo Lari. Compressing Highly Repetitive Binary Trees with an Application to Range Minimum Queries. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{carmona_et_al:LIPIcs.SEA.2026.10,
  author =	{Carmona, Gabriel and Lari, Filippo},
  title =	{{Compressing Highly Repetitive Binary Trees with an Application to Range Minimum Queries}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{10:1--10:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.10},
  URN =		{urn:nbn:de:0030-drops-260140},
  doi =		{10.4230/LIPIcs.SEA.2026.10},
  annote =	{Keywords: tree compression, range minimum query, compact data structures, algorithm engineering, experimental evaluation}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.5
Efficient Grammar Compression via RLZ-Based RePair

Authors: Rahul Varki, Travis Gagie, and Christina Boucher

Published in: LIPIcs, Volume 369, 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)

Abstract
Among grammar-based compression techniques, RePair is a notable offline encoding scheme known for its simplicity and powerful combinatorial properties, producing compact grammars by repeatedly replacing the most frequent adjacent pairs of symbols, known as bigrams. However, RePair’s memory usage scales poorly with input size, as it loads the entire text into memory. In contrast, Relative Lempel-Ziv (RLZ) parsing offers a scalable and lightweight online encoding scheme that losslessly represents a text in terms of phrases that refer to a reference string, but it often fails to expose deeper structural patterns. We introduce an algorithm that produces a RePair grammar from the RLZ parse of the input, leveraging the strengths of both methods. Our method, RLZ-RePair, performs bigram replacements systematically, preserving the integrity of the RLZ phrases throughout the RePair iterations. When the reference is well chosen, our method achieves the same grammar as standard RePair while significantly reducing both memory usage and the number of bigram replacements. In particular, we show that RLZ-RePair can reduce memory usage by more than 80% while incurring only a modest runtime increase compared to RePair. To our knowledge, RLZ-RePair is one of the first scalable methods that constructs exact RePair grammars, resulting in a grammar-based compressor that is both practical for large datasets and faithful to the theoretical elegance of RePair.
Cite as

Rahul Varki, Travis Gagie, and Christina Boucher. Efficient Grammar Compression via RLZ-Based RePair. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{varki_et_al:LIPIcs.CPM.2026.5,
  author =	{Varki, Rahul and Gagie, Travis and Boucher, Christina},
  title =	{{Efficient Grammar Compression via RLZ-Based RePair}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{5:1--5:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.5},
  URN =		{urn:nbn:de:0030-drops-259310},
  doi =		{10.4230/LIPIcs.CPM.2026.5},
  annote =	{Keywords: RePair, RLZ, Grammar Compression}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.32
Balancing Two-Dimensional Straight-Line Programs

Authors: Itai Boneh, Estéban Gabory, Paweł Gawrychowski, and Adam Górkiewicz

Published in: LIPIcs, Volume 369, 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)

Abstract
We consider building, given a straight-line program (SLP) consisting of g productions deriving a two-dimensional string T of size N× N, a structure capable of providing random access to any character of T. For one-dimensional strings, it is now known how to build a structure of size 𝒪(g) that provides random access in 𝒪(log N) time. In fact, it is known that this can be obtained by building an equivalent SLP of size 𝒪(g) and depth 𝒪(log N) [Ganardi, Jeż, Lohrey, JACM 2021]. We consider the analogous question for two-dimensional strings: can we build an equivalent SLP of roughly the same size and small depth? We show that the answer is negative: there exists an infinite family of two-dimensional strings of size N× N described by a 2D SLP of size g such that any 2D SLP of depth 𝒪(log N) describing the same string must be of size Ω(g⋅ N/log³N). We complement this with an upper bound showing how to construct such a 2D SLP of size 𝒪(g⋅ N). Next, we observe that one can naturally define a generalization of 2D SLP, which we call 2D SLP with holes. We show that a known general balancing theorem by [Ganardi, Jeż, Lohrey, JACM 2021] immediately implies that, given a 2D SLP of size g deriving a string of size N× N, we can construct a 2D SLP with holes of depth 𝒪(log N) and size 𝒪(g). This allows us to conclude that there is a structure of size 𝒪(g) providing random access in 𝒪(log N) time for such a 2D SLP. Further, this can be extended (analogously as for a 1D SLP) to obtain a structure of size 𝒪(g log^ε N) providing random access in 𝒪(log N/log log N) time, for any ε > 0. The same (optimal) random access time was very recently achieved by [De and Kempa, SODA 2026], but with a significantly larger structure of size 𝒪(g log^{2+ε} N).
Cite as

Itai Boneh, Estéban Gabory, Paweł Gawrychowski, and Adam Górkiewicz. Balancing Two-Dimensional Straight-Line Programs. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 32:1-32:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{boneh_et_al:LIPIcs.CPM.2026.32,
  author =	{Boneh, Itai and Gabory, Est\'{e}ban and Gawrychowski, Pawe{\l} and G\'{o}rkiewicz, Adam},
  title =	{{Balancing Two-Dimensional Straight-Line Programs}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{32:1--32:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.32},
  URN =		{urn:nbn:de:0030-drops-259582},
  doi =		{10.4230/LIPIcs.CPM.2026.32},
  annote =	{Keywords: Two-dimensional string, straight-line program, random access}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.31
On the Smallest Size of Internal Collage Systems

Authors: Soichiro Migita, Kyotaro Uehata, and Tomohiro I

Published in: LIPIcs, Volume 369, 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)

Abstract
A Straight-Line Program (SLP) for a string T is a context-free grammar in Chomsky normal form that derives T only, which can be seen as a compressed form of T. Kida et al. introduced collage systems [Theor. Comput. Sci., 2003] to generalize SLPs by adding repetition rules and truncation rules. The smallest size c(T) of collage systems for T has gained attention to see how these generalized rules improve the compression ability of SLPs. Navarro et al. [IEEE Trans. Inf. Theory, 2021] showed that c(T) ∈ O(z(T)) and there is a string family with c(T) ∈ Ω(b(T) log |T|), where z(T) is the number of phrases in the Lempel-Ziv parsing of T and b(T) is the smallest size of bidirectional schemes for T. They also introduced a subclass of collage systems, called internal collage systems, and proved that its smallest size ĉ(T) for T is at least b(T). While c(T) ≤ ĉ(T) is obvious, it is unknown how large ĉ(T) is compared to c(T). In this paper, we prove that ĉ(T) = Θ(c(T)) by showing that any collage system of size m can be transformed into an internal collage system of size O(m) in O(m²) time. Thanks to this result, we can focus on internal collage systems to study the asymptotic behavior of c(T), which helps to suppress excess use of truncation rules. As a direct application, we get b(T) = O(c(T)), which answers an open question posed in [Navarro et al., IEEE Trans. Inf. Theory, 2021]. We also give a MAX-SAT formulation to compute ĉ(T) for a given T.
Cite as

Soichiro Migita, Kyotaro Uehata, and Tomohiro I. On the Smallest Size of Internal Collage Systems. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{migita_et_al:LIPIcs.CPM.2026.31,
  author =	{Migita, Soichiro and Uehata, Kyotaro and I, Tomohiro},
  title =	{{On the Smallest Size of Internal Collage Systems}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.31},
  URN =		{urn:nbn:de:0030-drops-259575},
  doi =		{10.4230/LIPIcs.CPM.2026.31},
  annote =	{Keywords: Collage Systems, Dictionary-based compression, Compressibility measures}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.34
LZBE: An LZ-Style Compressor Supporting O(log n)-Time Random Access

Authors: Hiroki Shibata, Yuto Nakashima, Yutaro Yamaguchi, and Shunsuke Inenaga

Published in: LIPIcs, Volume 369, 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)

Abstract
An LZ-like factorization of a string divides it into factors, each being either a single character or a copy of a preceding substring. While grammar-based compression schemes support efficient random access with space linear in the compressed size, no comparable guarantees are known for general LZ-like factorizations. This limitation motivated restricted variants such as LZ-End [Kreft and Navarro, 2013] and height-bounded LZ (LZHB) [Bannai et al., 2024], which trade off some compression efficiency for faster access. In this paper, we introduce LZ-Begin-End (LZBE), a new LZ-like variant in which every copy factor must refer to a contiguous sequence of preceding factors. This structural restriction ensures that any context-free grammar can be transformed into an LZBE factorization of the same size. We further study the greedy LZBE factorization, which selects each copy factor to be as long as possible while processing the input from left to right, and show that it can be computed in linear time. Moreover, we exhibit a family of strings for which the greedy LZBE factorization is asymptotically smaller than the smallest grammar. These results demonstrate that the LZBE scheme is strictly more expressive than grammar-based compression in the worst case. To support fast queries, we propose a data structure for LZBE-compressed strings that permits O(log n)-time random access within space linear in the compressed size, where n is the length of the input string.
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Hiroki Shibata, Yuto Nakashima, Yutaro Yamaguchi, and Shunsuke Inenaga. LZBE: An LZ-Style Compressor Supporting O(log n)-Time Random Access. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 34:1-34:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{shibata_et_al:LIPIcs.CPM.2026.34,
  author =	{Shibata, Hiroki and Nakashima, Yuto and Yamaguchi, Yutaro and Inenaga, Shunsuke},
  title =	{{LZBE: An LZ-Style Compressor Supporting O(log n)-Time Random Access}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{34:1--34:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.34},
  URN =		{urn:nbn:de:0030-drops-259609},
  doi =		{10.4230/LIPIcs.CPM.2026.34},
  annote =	{Keywords: data compression, Lempel-Ziv parsing, string algorithms, random access}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.41
On the Complexity of Computing Strahler Numbers

Authors: Moses Ganardi and Markus Lohrey

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
It is shown that the problem of computing the Strahler number of a binary tree given as a term is complete for the circuit complexity class uniform NC¹. For several variants, where the binary tree is given by a pointer structure or in a succinct form by a directed acyclic graph or a tree straight-line program, the complexity of computing the Strahler number is determined as well. The problem, whether a given context-free grammar in Chomsky normal form produces a derivation tree (resp., an acyclic derivation tree), whose Strahler number is at least a given number k is shown to be P-complete (resp., PSPACE-complete).
Cite as

Moses Ganardi and Markus Lohrey. On the Complexity of Computing Strahler Numbers. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 41:1-41:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ganardi_et_al:LIPIcs.STACS.2026.41,
  author =	{Ganardi, Moses and Lohrey, Markus},
  title =	{{On the Complexity of Computing Strahler Numbers}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{41:1--41:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.41},
  URN =		{urn:nbn:de:0030-drops-255301},
  doi =		{10.4230/LIPIcs.STACS.2026.41},
  annote =	{Keywords: Strahler number, circuit complexity classes, context-free grammars}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.80
Efficient Compression in Semigroups

Authors: Alexander Thumm and Armin Weiß

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Straight-line programs are a central tool in several areas of computer science, including data compression, algebraic complexity theory, and the algorithmic solution of algebraic equations. In the algebraic setting, where straight-line programs can be interpreted as circuits over algebraic structures such as semigroups or groups, they have led to deep insights in computational complexity. A key result by Babai and Szemerédi (1984) showed that finite groups afford efficient compression via straight-line programs, enabling the design of a black-box computation model for groups. Building on their result, Fleischer (2019) placed the Cayley table membership problem for certain classes (pseudovarieties) of finite semigroups in NPOLYLOGTIME, and in some cases even in FOLL. He also provided a complete classification of pseudovarieties of finite monoids affording efficient compression. In this work, we complete this classification program initiated by Fleischer, characterizing precisely those pseudovarieties of finite semigroups that afford efficient compression via straight-line programs. Along the way, we also improve several known bounds on the length and width of straight-line programs over semigroups, monoids, and groups. These results lead to new upper bounds for the membership problem in the Cayley table model: for all pseudovarieties that afford efficient compression and do not contain any nonsolvable group, we obtain FOLL algorithms. In particular, we resolve a conjecture of Barrington, Kadau, Lange, and McKenzie (2001), showing that the membership problem for all solvable groups is in FOLL.
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Alexander Thumm and Armin Weiß. Efficient Compression in Semigroups. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 80:1-80:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{thumm_et_al:LIPIcs.STACS.2026.80,
  author =	{Thumm, Alexander and Wei{\ss}, Armin},
  title =	{{Efficient Compression in Semigroups}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{80:1--80:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.80},
  URN =		{urn:nbn:de:0030-drops-255694},
  doi =		{10.4230/LIPIcs.STACS.2026.80},
  annote =	{Keywords: Semigroups, straight-line programs, compression, membership problem}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.52
Unreliability in Practical Subclasses of Communicating Systems

Authors: Amrita Suresh and Nobuko Yoshida

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
Systems of communicating automata are prominent models for peer-to-peer message-passing over unbounded channels, but in the general scenario, most verification properties are undecidable. To address this issue, two decidable subclasses, Realisable with Synchronous Communication (RSC) and k-Multiparty Compatibility (k-MC), were proposed in the literature, with corresponding verification tools developed and applied in practice. Unfortunately, both RSC and k-MC are not resilient under failures: (1) their decidability relies on the assumption of perfect channels and (2) most standard protocols do not satisfy RSC or k-MC under failures. To address these limitations, this paper studies the resilience of RSC and k-MC under two distinct failure models: interference and crash-stop failures. For interference, we relax the conditions of RSC and k-MC and prove that the inclusions of these relaxed properties remain decidable under interference, preserving their known complexity bounds. We then propose a novel crash-handling communicating system that captures wider behaviours than existing multiparty session types (MPST) with crash-stop failures. We study a translation of MPST with crash-stop failures into this system integrating RSC and k-MC properties, and establish their decidability results. Finally, by verifying representative protocols from the literature using RSC and k-MC tools extended to interferences, we evaluate the relaxed systems and demonstrate their resilience.
Cite as

Amrita Suresh and Nobuko Yoshida. Unreliability in Practical Subclasses of Communicating Systems. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 52:1-52:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{suresh_et_al:LIPIcs.FSTTCS.2025.52,
  author =	{Suresh, Amrita and Yoshida, Nobuko},
  title =	{{Unreliability in Practical Subclasses of Communicating Systems}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{52:1--52:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.52},
  URN =		{urn:nbn:de:0030-drops-251312},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.52},
  annote =	{Keywords: Communicating automata, lossy channel, corruption, out of order, session types, crash-stop failure}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.9
Small Space Encoding and Recognition of k-Palindromic Prefixes

Authors: Gabriel Bathie, Jonas Ellert, and Tatiana Starikovskaya

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Palindromes are non-empty strings that read the same forward and backward. We study the problem of recognizing so-called k-palindromic strings, which can be represented as the concatenation of exactly k palindromes. [Rubinchik and Shur, MFCS 2020] showed that the problem is solvable in linear space and time. We present a read-only algorithm that recognizes all k-palindromic prefixes of a string T of length n in O(n ⋅ 6^{k²} ⋅ log^k n) time and O(6^{k²} ⋅ log^k n) space. As a corollary, we also obtain a read-only algorithm for computing the palindromic length of T, i.e., the smallest k such that T is k-palindromic, in O(n ⋅ 6^{k²} ⋅ log^⌈k/2⌉ n) time and O(6^{k²} ⋅ log^⌈k/2⌉ n) space.
Cite as

Gabriel Bathie, Jonas Ellert, and Tatiana Starikovskaya. Small Space Encoding and Recognition of k-Palindromic Prefixes. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bathie_et_al:LIPIcs.ISAAC.2025.9,
  author =	{Bathie, Gabriel and Ellert, Jonas and Starikovskaya, Tatiana},
  title =	{{Small Space Encoding and Recognition of k-Palindromic Prefixes}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{9:1--9:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.9},
  URN =		{urn:nbn:de:0030-drops-249178},
  doi =		{10.4230/LIPIcs.ISAAC.2025.9},
  annote =	{Keywords: palindromic length, read-only algorithms, palindromes}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.36
Streaming Periodicity with Mismatches, Wildcards, and Edits

Authors: Taha El Ghazi and Tatiana Starikovskaya

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
In this work, we study the problem of detecting periodic trends in strings. While detecting exact periodicity has been studied extensively, real-world data is often noisy, where small deviations or mismatches occur between repetitions. This work focuses on a generalized approach to period detection that efficiently handles noise. Given a string S of length n, the task is to identify integers p such that the prefix and the suffix of S, each of length n-p+1, are similar under a given distance measure. Ergün et al. [APPROX-RANDOM 2017] were the first to study this problem in the streaming model under the Hamming distance. In this work, we combine, in a non-trivial way, the Hamming distance sketch of Clifford et al. [SODA 2019] and the structural description of the k-mismatch occurrences of a pattern in a text by Charalampopoulos et al. [FOCS 2020] to present a more efficient streaming algorithm for period detection under the Hamming distance. As a corollary, we derive a streaming algorithm for detecting periods of strings which may contain wildcards, a special symbol that match any character of the alphabet. Our algorithm is not only more efficient than that of Ergün et al. [TCS 2020], but it also operates without their assumption that the string must be free of wildcards in its final characters. Additionally, we introduce the first two-pass streaming algorithm for computing periods under the edit distance by leveraging and extending the Bhattacharya-Koucký’s grammar decomposition technique [STOC 2023].
Cite as

Taha El Ghazi and Tatiana Starikovskaya. Streaming Periodicity with Mismatches, Wildcards, and Edits. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 36:1-36:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{elghazi_et_al:LIPIcs.ISAAC.2025.36,
  author =	{El Ghazi, Taha and Starikovskaya, Tatiana},
  title =	{{Streaming Periodicity with Mismatches, Wildcards, and Edits}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{36:1--36:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.36},
  URN =		{urn:nbn:de:0030-drops-249446},
  doi =		{10.4230/LIPIcs.ISAAC.2025.36},
  annote =	{Keywords: approximate periods, pattern matching, streaming algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.15
Certified Implementability of Global Multiparty Protocols

Authors: Elaine Li and Thomas Wies

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Implementability is the decision problem at the heart of top-down approaches to protocol verification. In this paper, we present a mechanization of a recently proposed precise implementability characterization by Li et al. for a large class of protocols that subsumes many existing formalisms in the literature. Our protocols and implementations model asynchronous commmunication, and can exhibit infinite behavior. We improve upon their pen-and-paper results by unifying distinct formalisms, simplifying existing proof arguments, elaborating on the construction of canonical implementations, and even uncovering a subtle bug in the semantics for infinite words. As a corollary of our mechanization, we show that the original characterization of implementability applies even to protocols with infinitely many participants. We also contribute a reusable library for reasoning about generic communicating state machines. Our mechanization consists of about 15k lines of Rocq code. We believe that our mechanization can provide the foundation for deductively proving the implementability of protocols beyond the reach of prior work, extracting certified implementations for finite protocols, and investigating implementability under alternative asynchronous communication models.
Cite as

Elaine Li and Thomas Wies. Certified Implementability of Global Multiparty Protocols. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 15:1-15:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{li_et_al:LIPIcs.ITP.2025.15,
  author =	{Li, Elaine and Wies, Thomas},
  title =	{{Certified Implementability of Global Multiparty Protocols}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{15:1--15:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.15},
  URN =		{urn:nbn:de:0030-drops-246139},
  doi =		{10.4230/LIPIcs.ITP.2025.15},
  annote =	{Keywords: Asynchronous protocols, communicating state machines, labeled transition systems, infinite semantics, realizability, multiparty session types, choreographies, deadlock freedom}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.51
Word Structures and Their Automatic Presentations

Authors: Xiaoyang Gong, Bakh Khoussainov, and Yuyang Zhuge

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
We study automatic presentations of the structures (ℕ; S), (ℕ; E_S), (ℕ; ≤), and their expansions by a unary predicate U. Here S is the successor function, E_S is the undirected version of S, and ≤ is the natural order. We call these structures word structures. Our goal is three-fold. First, we study the isomorphism problem for automatic word structures by focusing on the following three problems. The first problem asks to design an algorithm that, given an automatic structure A, decides if A is isomorphic to (ℕ; S). The second asks to design an algorithm that, given two automatic presentations of (ℕ; S, U₁) and (ℕ; S, U₂), where U₁ and U₂ are unary predicates, decides if these structures are isomorphic. The third problem investigates if there is an algorithm that, given two automatic presentations of (ℕ; ≤, U₁) and (ℕ; ≤, U₂), decides whether U₁ ∩ U₂ ≠ ∅. We show that these problems are undecidable. Next, we study intrinsic regularity of the function S in the structure Path_ω = (ℕ; E_S). We build an automatic presentation of Path_ω in which S is not regular. This implies that S is not intrinsically regular in Path_ω. For U ⊆ ℕ, let d_U be the function that computes the distances between the consecutive elements of U. We build automatic presentations of (ℕ; ≤, U) where d_U can realise logarithmic, radical, intermediate, and exponential functions.
Cite as

Xiaoyang Gong, Bakh Khoussainov, and Yuyang Zhuge. Word Structures and Their Automatic Presentations. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 51:1-51:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gong_et_al:LIPIcs.MFCS.2025.51,
  author =	{Gong, Xiaoyang and Khoussainov, Bakh and Zhuge, Yuyang},
  title =	{{Word Structures and Their Automatic Presentations}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{51:1--51:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.51},
  URN =		{urn:nbn:de:0030-drops-241581},
  doi =		{10.4230/LIPIcs.MFCS.2025.51},
  annote =	{Keywords: Automatic structures, the isomorphism problem, decidability, undecidability, regular relations}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.69
FO-Query Enumeration over SLP-Compressed Structures of Bounded Degree

Authors: Markus Lohrey, Sebastian Maneth, and Markus L. Schmid

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Enumerating the result set of a first-order query over a relational structure of bounded degree can be done with linear preprocessing and constant delay. In this work, we extend this result towards the compressed perspective where the structure is given in a potentially highly compressed form by a straight-line program (SLP). Our main result is an algorithm that enumerates the result set of a first-order query over a structure of bounded degree that is represented by an SLP satisfying the so-called apex condition. For a fixed formula, the enumeration algorithm has constant delay and needs a preprocessing time that is linear in the size of the SLP.
Cite as

Markus Lohrey, Sebastian Maneth, and Markus L. Schmid. FO-Query Enumeration over SLP-Compressed Structures of Bounded Degree. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 69:1-69:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lohrey_et_al:LIPIcs.MFCS.2025.69,
  author =	{Lohrey, Markus and Maneth, Sebastian and Schmid, Markus L.},
  title =	{{FO-Query Enumeration over SLP-Compressed Structures of Bounded Degree}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{69:1--69:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.69},
  URN =		{urn:nbn:de:0030-drops-241760},
  doi =		{10.4230/LIPIcs.MFCS.2025.69},
  annote =	{Keywords: Enumeration algorithms, FO-logic, query evaluation over compressed data}
}
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