Laura Bozzelli , Angelo Montanari , Adriano Peron , Pietro Sala
{"title":"Pspace-completeness of the temporal logic of sub-intervals and suffixes","authors":"Laura Bozzelli , Angelo Montanari , Adriano Peron , Pietro Sala","doi":"10.1016/j.ic.2023.105083","DOIUrl":"https://doi.org/10.1016/j.ic.2023.105083","url":null,"abstract":"<div><p>In this paper, we prove <span>Pspace</span>-completeness of the finite satisfiability and model checking problems for the fragment of Halpern and Shoham interval logic with modality <span><math><mrow><mi>〈</mi><mi>E</mi><mi>〉</mi></mrow></math></span>, for the “suffix” relation on pairs of intervals, and modality <span><math><mrow><mi>〈</mi><mi>D</mi><mi>〉</mi></mrow></math></span>, for the “sub-interval” relation, under the homogeneity assumption. The result significantly improves the <span>Expspace</span> upper bound recently established for the same fragment, and proves the rather surprising fact that the complexity of the considered problems does not change when we add either the modality for suffixes (<span><math><mrow><mi>〈</mi><mi>E</mi><mi>〉</mi></mrow></math></span>) or, symmetrically, the modality for prefixes (<span><math><mrow><mi>〈</mi><mi>B</mi><mi>〉</mi></mrow></math></span>) to the logic of sub-intervals (featuring only <span><math><mrow><mi>〈</mi><mi>D</mi><mi>〉</mi></mrow></math></span>).</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"294 ","pages":"Article 105083"},"PeriodicalIF":1.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49871263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Taming Strategy Logic: Non-Recurrent Fragments","authors":"Massimo Benerecetti, Fabio Mogavero, Adriano Peron","doi":"10.1016/j.ic.2023.105081","DOIUrl":"https://doi.org/10.1016/j.ic.2023.105081","url":null,"abstract":"<div><p><em>Strategy Logic</em> (<figure><img></figure> for short) is one of the prominent languages for reasoning about the strategic abilities of agents in a multi-agent setting. This logic extends <figure><img></figure> with first-order quantifiers over the agent strategies and encompasses other formalisms, such as <figure><img></figure> and <figure><img></figure>. The <em>model-checking problem</em> for <figure><img></figure> and several of its fragments has been extensively studied. On the other hand, the picture is much less clear on the satisfiability front, where the problem is undecidable for the full logic. In this work, we study two fragments of <em>One-Goal</em> <figure><img></figure>, where the nesting of sentences within temporal operators is constrained. We show that the <em>satisfiability problem</em> for these two logics, and for the corresponding fragments of <figure><img></figure> and <figure><img></figure>, is in <figure><img></figure> and <figure><img></figure>, respectively.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"294 ","pages":"Article 105081"},"PeriodicalIF":1.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49871267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the complexity of decision problems for some classes of machines and applications","authors":"Oscar H. Ibarra , Ian McQuillan","doi":"10.1016/j.ic.2023.105080","DOIUrl":"https://doi.org/10.1016/j.ic.2023.105080","url":null,"abstract":"<div><p><span>We study the computational complexity<span> of important decision problems — including general membership, fixed-machine membership, emptiness, disjointness<span>, equivalence, containment, universe, and finiteness problems — for various restrictions and combinations of two-way nondeterministic reversal-bounded multicounter machines (</span></span></span><span><math><mn>2</mn><mrow><mi>NCM</mi></mrow></math></span><span>) and two-way pushdown automata. We show that the general membership problem (respectively fixed membership problem) for </span><span><math><mn>2</mn><mrow><mi>NCM</mi></mrow></math></span> is <span><math><mi>NP</mi></math></span>-complete (respectively in <span><math><mi>P</mi></math></span>).</p><p>We then give applications to some problems in coding theory. We examine generalizations of various types of codes with marginal errors. For example, a language <em>L</em> is <em>k</em>-infix-free if there is no non-empty string <em>y</em> in <em>L</em> that is an infix of more than <em>k</em> strings in <span><math><mi>L</mi><mo>−</mo><mo>{</mo><mi>y</mi><mo>}</mo></math></span>. Our general results imply the complexity of determining whether a given machine accepts a <em>k</em><span>-infix-free language, for one- and two-way deterministic and nondeterministic finite automata (answering an open question from the literature).</span></p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"294 ","pages":"Article 105080"},"PeriodicalIF":1.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49871270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Extending the reach of the point-to-set principle","authors":"Jack H. Lutz , Neil Lutz , Elvira Mayordomo","doi":"10.1016/j.ic.2023.105078","DOIUrl":"https://doi.org/10.1016/j.ic.2023.105078","url":null,"abstract":"<div><p>The <em>point-to-set principle</em> of J. Lutz and N. Lutz (2018) has recently enabled the theory of computing to be used to answer open questions about fractal geometry in Euclidean spaces <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. These are classical questions, meaning that their statements do not involve computation or related aspects of logic.</p><p>In this paper we extend the <em>reach</em> of the point-to-set principle from Euclidean spaces to arbitrary separable metric spaces <em>X</em>. We first extend two algorithmic dimensions—computability-theoretic versions of classical Hausdorff and packing dimensions that assign dimensions <span><math><mi>dim</mi><mo></mo><mo>(</mo><mi>x</mi><mo>)</mo></math></span> and <span><math><mrow><mi>Dim</mi></mrow><mo>(</mo><mi>x</mi><mo>)</mo></math></span> to <em>individual points</em> <span><math><mi>x</mi><mo>∈</mo><mi>X</mi></math></span>—to arbitrary separable metric spaces and to arbitrary gauge families. Our first two main results then extend the point-to-set principle to arbitrary separable metric spaces and to a large class of gauge families.</p><p>We demonstrate the power of our extended point-to-set principle by using it to prove new theorems about classical fractal dimensions in hyperspaces.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"294 ","pages":"Article 105078"},"PeriodicalIF":1.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49870998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The tail-recursive fragment of timed recursive CTL","authors":"Florian Bruse, Martin Lange","doi":"10.1016/j.ic.2023.105084","DOIUrl":"https://doi.org/10.1016/j.ic.2023.105084","url":null,"abstract":"<div><p>Timed Recursive CTL (TRCTL) was recently proposed as a merger of two extensions of the well-known branching-time logic CTL: Timed CTL on one hand is interpreted over real-time systems like timed automata, and Recursive CTL (RecCTL) on the other hand obtains high expressiveness through the introduction of a recursion operator. Model checking for the resulting logic is known to be 2-EXPTIME-complete.</p><p><span><span>The aim of this paper is to investigate the possibility to obtain a fragment of lower complexity without losing too much expressive power. It is obtained by a </span>syntactic property called “tail-recursiveness” that restricts the way that </span>recursive formulas can be built. This restriction is known to decrease the complexity of model checking by half an exponential in the untimed setting. We show that this also works in the real-time world: model checking for the tail-recursive fragment of TRCTL is EXPSPACE-complete already in its data complexity, i.e. for a fixed formula. The upper bound is obtained via a model-checking procedure on region graphs combining standard untiming constructions with a tailored algorithm. The lower bound is established by a reduction from a suitable tiling problem.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"294 ","pages":"Article 105084"},"PeriodicalIF":1.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49871262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Raffaele Giancarlo , Giovanni Manzini , Antonio Restivo , Giovanna Rosone , Marinella Sciortino
{"title":"A new class of string transformations for compressed text indexing","authors":"Raffaele Giancarlo , Giovanni Manzini , Antonio Restivo , Giovanna Rosone , Marinella Sciortino","doi":"10.1016/j.ic.2023.105068","DOIUrl":"https://doi.org/10.1016/j.ic.2023.105068","url":null,"abstract":"<div><p>Introduced about thirty years ago in the field of data compression, the Burrows-Wheeler Transform (BWT) is a string transformation that, besides being a <em>booster</em> of the performance of memoryless compressors, plays a fundamental role in the design of efficient self-indexing compressed data structures. Finding other string transformations with the same remarkable properties of BWT has been a challenge for many researchers for a long time. In this paper, we introduce a whole class of new string transformations, called <em>local orderings-based transformations</em>, which have all the “myriad virtues” of BWT. As a further result, we show that such new string transformations can be used for the construction of the recently introduced <em>r</em>-index, which makes them suitable also for highly repetitive collections. In this context, we consider the problem of finding, for a given string, the BWT variant that minimizes the number of runs in the transformed string.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"294 ","pages":"Article 105068"},"PeriodicalIF":1.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49871269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bideterministic weighted automata","authors":"Peter Kostolányi","doi":"10.1016/j.ic.2023.105093","DOIUrl":"https://doi.org/10.1016/j.ic.2023.105093","url":null,"abstract":"<div><p>A finite automaton<span><span> is called bideterministic if it is both deterministic and codeterministic – that is, if it is deterministic and its transpose is deterministic as well. The study of such automata in a weighted setting is initiated. All trim bideterministic weighted automata over integral domains and over positive semirings are proved to be minimal. On the contrary, it is observed that this property does not hold over </span>commutative rings in general: non-minimal trim bideterministic weighted automata do exist over all semirings that are not zero-divisor free, and over many such semirings, these automata might not even admit equivalents that are both minimal and bideterministic. The problem of determining whether a given rational series is realised by a bideterministic automaton is shown to be decidable over fields and over tropical semirings. An example of a positive semiring over which this problem becomes undecidable is given as well.</span></p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"295 ","pages":"Article 105093"},"PeriodicalIF":1.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49889702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Weighted two-way transducers","authors":"Fan Feng, Andreas Maletti","doi":"10.1016/j.ic.2023.105094","DOIUrl":"https://doi.org/10.1016/j.ic.2023.105094","url":null,"abstract":"<div><p>Weighted two-way transducers over complete commutative semirings are introduced and investigated. Their computed mappings have two-way definable support. Conversely, for every two-way definable relation <em>R</em> there exists a mapping that has support <em>R</em><span> and is computable by a weighted two-way transducer. The class of all such computed mappings is naturally closed under sum. Finally, both the subclass computed by deterministic weighted two-way transducers and the subclass computed by unambiguous weighted two-way transducers are shown to be closed under composition, pseudo </span><span>Hadamard</span> product, unambiguous <span>Cauchy</span> product, and unambiguous <span>Kleene</span> iteration.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"295 ","pages":"Article 105094"},"PeriodicalIF":1.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49889704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Online search with a hint","authors":"Spyros Angelopoulos","doi":"10.1016/j.ic.2023.105091","DOIUrl":"https://doi.org/10.1016/j.ic.2023.105091","url":null,"abstract":"<div><p>We introduce the study of search problems, in a setting in which the searcher has some information, or <em>hint</em> concerning the hiding target. In particular, we focus on one of the fundamental problems in search theory, namely the <em>linear search</em> problem. Here, an immobile target is hidden at some unknown position on an unbounded line, and a mobile searcher, initially positioned at some specific point of the line called the <em>root</em>, must traverse the line so as to locate the target. The objective is to minimize the worst-case ratio of the distance traversed by the searcher to the distance of the target from the root, which is known as the <span><em>competitive ratio</em></span> of the search.</p><p>We consider three settings in regards to the nature of the hint: i) the hint suggests the exact position of the target on the line; ii) the hint suggests the direction of the optimal search (i.e., to the left or the right of the root); and iii) the hint is a general <em>k</em>-bit string that encodes some information concerning the target. Our objective is to study the <em>Pareto</em>-efficiency of strategies in this model, with respect to the tradeoff between <em>consistency</em> and <em>robustness</em>. Namely, we seek optimal, or near-optimal tradeoffs between the searcher's performance if the hint is correct (i.e., provided by a trusted source) and if the hint is incorrect (i.e., provided by an adversary).</p><p>We prove several results in each of these three settings. For positional hints, we show that the optimal consistency of <em>r</em>-robust strategies is <span><math><mo>(</mo><msub><mrow><mi>b</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>+</mo><mn>1</mn><mo>)</mo><mo>/</mo><mo>(</mo><msub><mrow><mi>b</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>−</mo><mn>1</mn><mo>)</mo></math></span>, where <span><math><msub><mrow><mi>b</mi></mrow><mrow><mi>r</mi></mrow></msub></math></span> is defined to be equal to <span><math><mfrac><mrow><msub><mrow><mi>ρ</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>+</mo><msqrt><mrow><msubsup><mrow><mi>ρ</mi></mrow><mrow><mi>r</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>−</mo><mn>4</mn><msub><mrow><mi>ρ</mi></mrow><mrow><mi>r</mi></mrow></msub></mrow></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>, and <span><math><msub><mrow><mi>ρ</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>=</mo><mo>(</mo><mi>r</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>/</mo><mn>2</mn></math></span>, for all <span><math><mi>r</mi><mo>≥</mo><mn>9</mn></math></span>. For directional hints, we show that for every <span><math><mi>b</mi><mo>≥</mo><mn>1</mn></math></span> and <span><math><mi>δ</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>, there exists a strategy with consistency equal to <span><math><mi>c</mi><mo>=</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>(</mo><mfrac><mrow><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><msup><mrow><mi>b</mi></mrow><mrow><mn>2</m","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"295 ","pages":"Article 105091"},"PeriodicalIF":1.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49889703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Synchronizing deterministic push-down automata can be really hard","authors":"Henning Fernau , Petra Wolf , Tomoyuki Yamakami","doi":"10.1016/j.ic.2023.105089","DOIUrl":"https://doi.org/10.1016/j.ic.2023.105089","url":null,"abstract":"<div><p><span><span>The question if a deterministic finite automaton<span> admits a software reset in the form of a so-called synchronizing word can be answered in polynomial time<span>. In this paper, we extend this algorithmic question to deterministic automata beyond </span></span></span>finite automata<span>. We prove that the question of synchronizability becomes undecidable even when looking at deterministic one-counter automata. This is also true for another classical mild extension of regularity, namely, that of deterministic one-turn push-down automata. However, when we combine both restrictions, we arrive at scenarios with a </span></span><span>PSPACE</span>-complete (and hence decidable) synchronizability problem. Likewise, we arrive at a decidable synchronizability problem for (partially) blind deterministic counter automata.</p><p>There are several interpretations of what <em>synchronizability</em><span> should mean for deterministic push-down automata. This is depending on the role of the stack: should it be empty on synchronization, should it be always the same or is it arbitrary? For the automata classes studied in this paper, the complexity or decidability status of the synchronizability problem is mostly independent of this technicality, but we also discuss one class of automata where this makes a difference.</span></p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"295 ","pages":"Article 105089"},"PeriodicalIF":1.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49889752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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