--- _id: '5437' abstract: - lang: eng text: "We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean-payoff property, the ratio property, and the minimum initial credit for energy property. \r\nThe algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with constant treewidth, and it is well-known that the control-flow graphs of most programs have constant treewidth. Let $n$ denote the number of nodes of a graph, $m$ the number of edges (for constant treewidth graphs $m=O(n)$) and $W$ the largest absolute value of the weights.\r\nOur main theoretical results are as follows.\r\nFirst, for constant treewidth graphs we present an algorithm that approximates the mean-payoff value within a multiplicative factor of $\\epsilon$ in time $O(n \\cdot \\log (n/\\epsilon))$ and linear space, as compared to the classical algorithms that require quadratic time. Second, for the ratio property we present an algorithm that for constant treewidth graphs works in time $O(n \\cdot \\log (|a\\cdot b|))=O(n\\cdot\\log (n\\cdot W))$, when the output is $\\frac{a}{b}$, as compared to the previously best known algorithm with running time $O(n^2 \\cdot \\log (n\\cdot W))$. Third, for the minimum initial credit problem we show that (i)~for general graphs the problem can be solved in $O(n^2\\cdot m)$ time and the associated decision problem can be solved in $O(n\\cdot m)$ time, improving the previous known $O(n^3\\cdot m\\cdot \\log (n\\cdot W))$ and $O(n^2 \\cdot m)$ bounds, respectively; and (ii)~for constant treewidth graphs we present an algorithm that requires $O(n\\cdot \\log n)$ time, improving the previous known $O(n^4 \\cdot \\log (n \\cdot W))$ bound.\r\nWe have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks. " alternative_title: - IST Austria Technical Report author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Rasmus full_name: Ibsen-Jensen, Rasmus id: 3B699956-F248-11E8-B48F-1D18A9856A87 last_name: Ibsen-Jensen orcid: 0000-0003-4783-0389 - first_name: Andreas full_name: Pavlogiannis, Andreas id: 49704004-F248-11E8-B48F-1D18A9856A87 last_name: Pavlogiannis orcid: 0000-0002-8943-0722 citation: ama: Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs. IST Austria; 2015. doi:10.15479/AT:IST-2015-330-v2-1 apa: Chatterjee, K., Ibsen-Jensen, R., & Pavlogiannis, A. (2015). Faster algorithms for quantitative verification in constant treewidth graphs. IST Austria. https://doi.org/10.15479/AT:IST-2015-330-v2-1 chicago: Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, and Andreas Pavlogiannis. Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs. IST Austria, 2015. https://doi.org/10.15479/AT:IST-2015-330-v2-1. ieee: K. Chatterjee, R. Ibsen-Jensen, and A. Pavlogiannis, Faster algorithms for quantitative verification in constant treewidth graphs. IST Austria, 2015. ista: Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. 2015. Faster algorithms for quantitative verification in constant treewidth graphs, IST Austria, 27p. mla: Chatterjee, Krishnendu, et al. Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs. IST Austria, 2015, doi:10.15479/AT:IST-2015-330-v2-1. short: K. Chatterjee, R. Ibsen-Jensen, A. Pavlogiannis, Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs, IST Austria, 2015. date_created: 2018-12-12T11:39:19Z date_published: 2015-04-27T00:00:00Z date_updated: 2023-02-23T12:26:05Z day: '27' ddc: - '000' department: - _id: KrCh doi: 10.15479/AT:IST-2015-330-v2-1 file: - access_level: open_access checksum: f5917c20f84018b362d385c000a2e123 content_type: application/pdf creator: system date_created: 2018-12-12T11:53:12Z date_updated: 2020-07-14T12:46:54Z file_id: '5473' file_name: IST-2015-330-v2+1_main.pdf file_size: 1072137 relation: main_file file_date_updated: 2020-07-14T12:46:54Z has_accepted_license: '1' language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: '27' publication_identifier: issn: - 2664-1690 publication_status: published publisher: IST Austria pubrep_id: '333' related_material: record: - id: '1607' relation: later_version status: public - id: '5430' relation: earlier_version status: public status: public title: Faster algorithms for quantitative verification in constant treewidth graphs type: technical_report user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2015' ... --- _id: '5430' abstract: - lang: eng text: We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean- payoff property, the ratio property, and the minimum initial credit for energy property. The algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with constant treewidth, and it is well-known that the control-flow graphs of most programs have constant treewidth. Let n denote the number of nodes of a graph, m the number of edges (for constant treewidth graphs m = O ( n ) ) and W the largest absolute value of the weights. Our main theoretical results are as follows. First, for constant treewidth graphs we present an algorithm that approximates the mean-payoff value within a mul- tiplicative factor of ∊ in time O ( n · log( n/∊ )) and linear space, as compared to the classical algorithms that require quadratic time. Second, for the ratio property we present an algorithm that for constant treewidth graphs works in time O ( n · log( | a · b · n | )) = O ( n · log( n · W )) , when the output is a b , as compared to the previously best known algorithm with running time O ( n 2 · log( n · W )) . Third, for the minimum initial credit problem we show that (i) for general graphs the problem can be solved in O ( n 2 · m ) time and the associated decision problem can be solved in O ( n · m ) time, improving the previous known O ( n 3 · m · log( n · W )) and O ( n 2 · m ) bounds, respectively; and (ii) for constant treewidth graphs we present an algorithm that requires O ( n · log n ) time, improving the previous known O ( n 4 · log( n · W )) bound. We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks. alternative_title: - IST Austria Technical Report author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Rasmus full_name: Ibsen-Jensen, Rasmus id: 3B699956-F248-11E8-B48F-1D18A9856A87 last_name: Ibsen-Jensen orcid: 0000-0003-4783-0389 - first_name: Andreas full_name: Pavlogiannis, Andreas id: 49704004-F248-11E8-B48F-1D18A9856A87 last_name: Pavlogiannis orcid: 0000-0002-8943-0722 citation: ama: Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs. IST Austria; 2015. doi:10.15479/AT:IST-2015-319-v1-1 apa: Chatterjee, K., Ibsen-Jensen, R., & Pavlogiannis, A. (2015). Faster algorithms for quantitative verification in constant treewidth graphs. IST Austria. https://doi.org/10.15479/AT:IST-2015-319-v1-1 chicago: Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, and Andreas Pavlogiannis. Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs. IST Austria, 2015. https://doi.org/10.15479/AT:IST-2015-319-v1-1. ieee: K. Chatterjee, R. Ibsen-Jensen, and A. Pavlogiannis, Faster algorithms for quantitative verification in constant treewidth graphs. IST Austria, 2015. ista: Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. 2015. Faster algorithms for quantitative verification in constant treewidth graphs, IST Austria, 31p. mla: Chatterjee, Krishnendu, et al. Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs. IST Austria, 2015, doi:10.15479/AT:IST-2015-319-v1-1. short: K. Chatterjee, R. Ibsen-Jensen, A. Pavlogiannis, Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs, IST Austria, 2015. date_created: 2018-12-12T11:39:17Z date_published: 2015-02-10T00:00:00Z date_updated: 2023-02-23T12:26:22Z day: '10' ddc: - '000' department: - _id: KrCh doi: 10.15479/AT:IST-2015-319-v1-1 file: - access_level: open_access checksum: 62c6ea01e342553dcafb88a070fb1ad5 content_type: application/pdf creator: system date_created: 2018-12-12T11:53:21Z date_updated: 2020-07-14T12:46:52Z file_id: '5482' file_name: IST-2015-319-v1+1_long.pdf file_size: 1089651 relation: main_file file_date_updated: 2020-07-14T12:46:52Z has_accepted_license: '1' language: - iso: eng month: '02' oa: 1 oa_version: Published Version page: '31' publication_identifier: issn: - 2664-1690 publication_status: published publisher: IST Austria pubrep_id: '319' related_material: record: - id: '1607' relation: later_version status: public - id: '5437' relation: later_version status: public status: public title: Faster algorithms for quantitative verification in constant treewidth graphs type: technical_report user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2015' ... --- _id: '5439' abstract: - lang: eng text: 'The target discounted-sum problem is the following: Given a rational discount factor 0 < λ < 1 and three rational values a, b, and t, does there exist a finite or an infinite sequence w ε(a, b)∗ or w ε(a, b)w, such that Σ|w| i=0 w(i)λi equals t? The problem turns out to relate to many fields of mathematics and computer science, and its decidability question is surprisingly hard to solve. We solve the finite version of the problem, and show the hardness of the infinite version, linking it to various areas and open problems in mathematics and computer science: β-expansions, discounted-sum automata, piecewise affine maps, and generalizations of the Cantor set. We provide some partial results to the infinite version, among which are solutions to its restriction to eventually-periodic sequences and to the cases that λ λ 1/2 or λ = 1/n, for every n ε N. We use our results for solving some open problems on discounted-sum automata, among which are the exact-value problem for nondeterministic automata over finite words and the universality and inclusion problems for functional automata. ' alternative_title: - IST Austria Technical Report author: - first_name: Udi full_name: Boker, Udi id: 31E297B6-F248-11E8-B48F-1D18A9856A87 last_name: Boker - first_name: Thomas A full_name: Henzinger, Thomas A id: 40876CD8-F248-11E8-B48F-1D18A9856A87 last_name: Henzinger orcid: 0000−0002−2985−7724 - first_name: Jan full_name: Otop, Jan id: 2FC5DA74-F248-11E8-B48F-1D18A9856A87 last_name: Otop citation: ama: Boker U, Henzinger TA, Otop J. The Target Discounted-Sum Problem. IST Austria; 2015. doi:10.15479/AT:IST-2015-335-v1-1 apa: Boker, U., Henzinger, T. A., & Otop, J. (2015). The target discounted-sum problem. IST Austria. https://doi.org/10.15479/AT:IST-2015-335-v1-1 chicago: Boker, Udi, Thomas A Henzinger, and Jan Otop. The Target Discounted-Sum Problem. IST Austria, 2015. https://doi.org/10.15479/AT:IST-2015-335-v1-1. ieee: U. Boker, T. A. Henzinger, and J. Otop, The target discounted-sum problem. IST Austria, 2015. ista: Boker U, Henzinger TA, Otop J. 2015. The target discounted-sum problem, IST Austria, 20p. mla: Boker, Udi, et al. The Target Discounted-Sum Problem. IST Austria, 2015, doi:10.15479/AT:IST-2015-335-v1-1. short: U. Boker, T.A. Henzinger, J. Otop, The Target Discounted-Sum Problem, IST Austria, 2015. date_created: 2018-12-12T11:39:20Z date_published: 2015-05-18T00:00:00Z date_updated: 2023-02-23T10:08:48Z day: '18' ddc: - '004' - '512' - '513' department: - _id: ToHe doi: 10.15479/AT:IST-2015-335-v1-1 file: - access_level: open_access checksum: 40405907aa012acece1bc26cf0be554d content_type: application/pdf creator: system date_created: 2018-12-12T11:53:55Z date_updated: 2020-07-14T12:46:55Z file_id: '5517' file_name: IST-2015-335-v1+1_report.pdf file_size: 589619 relation: main_file file_date_updated: 2020-07-14T12:46:55Z has_accepted_license: '1' language: - iso: eng month: '05' oa: 1 oa_version: Published Version page: '20' publication_identifier: issn: - 2664-1690 publication_status: published publisher: IST Austria pubrep_id: '335' related_material: record: - id: '1659' relation: later_version status: public status: public title: The target discounted-sum problem type: technical_report user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2015' ... --- _id: '5438' abstract: - lang: eng text: "The edit distance between two words w1, w2 is the minimal number of word operations (letter insertions, deletions, and substitutions) necessary to transform w1 to w2. The edit distance generalizes to languages L1, L2, where the edit distance is the minimal number k such that for every word from L1 there exists a word in L2 with edit distance at most k. We study the edit distance computation problem between pushdown automata and their subclasses.\r\nThe problem of computing edit distance to a pushdown automaton is undecidable, and in practice, the interesting question is to compute the edit distance from a pushdown automaton (the implementation, a standard model for programs with recursion) to a regular language (the specification). In this work, we present a complete picture of decidability and complexity for deciding whether, for a given threshold k, the edit distance from a pushdown automaton to a finite automaton is at most k. " alternative_title: - IST Austria Technical Report author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Thomas A full_name: Henzinger, Thomas A id: 40876CD8-F248-11E8-B48F-1D18A9856A87 last_name: Henzinger orcid: 0000−0002−2985−7724 - first_name: Rasmus full_name: Ibsen-Jensen, Rasmus id: 3B699956-F248-11E8-B48F-1D18A9856A87 last_name: Ibsen-Jensen orcid: 0000-0003-4783-0389 - first_name: Jan full_name: Otop, Jan id: 2FC5DA74-F248-11E8-B48F-1D18A9856A87 last_name: Otop citation: ama: Chatterjee K, Henzinger TA, Ibsen-Jensen R, Otop J. Edit Distance for Pushdown Automata. IST Austria; 2015. doi:10.15479/AT:IST-2015-334-v1-1 apa: Chatterjee, K., Henzinger, T. A., Ibsen-Jensen, R., & Otop, J. (2015). Edit distance for pushdown automata. IST Austria. https://doi.org/10.15479/AT:IST-2015-334-v1-1 chicago: Chatterjee, Krishnendu, Thomas A Henzinger, Rasmus Ibsen-Jensen, and Jan Otop. Edit Distance for Pushdown Automata. IST Austria, 2015. https://doi.org/10.15479/AT:IST-2015-334-v1-1. ieee: K. Chatterjee, T. A. Henzinger, R. Ibsen-Jensen, and J. Otop, Edit distance for pushdown automata. IST Austria, 2015. ista: Chatterjee K, Henzinger TA, Ibsen-Jensen R, Otop J. 2015. Edit distance for pushdown automata, IST Austria, 15p. mla: Chatterjee, Krishnendu, et al. Edit Distance for Pushdown Automata. IST Austria, 2015, doi:10.15479/AT:IST-2015-334-v1-1. short: K. Chatterjee, T.A. Henzinger, R. Ibsen-Jensen, J. Otop, Edit Distance for Pushdown Automata, IST Austria, 2015. date_created: 2018-12-12T11:39:20Z date_published: 2015-05-05T00:00:00Z date_updated: 2023-02-23T12:20:08Z day: '05' ddc: - '004' department: - _id: KrCh doi: 10.15479/AT:IST-2015-334-v1-1 file: - access_level: open_access checksum: 8a5f2d77560e552af87eb1982437a43b content_type: application/pdf creator: system date_created: 2018-12-12T11:53:56Z date_updated: 2020-07-14T12:46:55Z file_id: '5518' file_name: IST-2015-334-v1+1_report.pdf file_size: 422573 relation: main_file file_date_updated: 2020-07-14T12:46:55Z has_accepted_license: '1' language: - iso: eng month: '05' oa: 1 oa_version: Published Version page: '15' publication_identifier: issn: - 2664-1690 publication_status: published publisher: IST Austria pubrep_id: '334' related_material: record: - id: '1610' relation: later_version status: public - id: '465' relation: later_version status: public status: public title: Edit distance for pushdown automata type: technical_report user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2015' ... --- _id: '5440' abstract: - lang: eng text: 'Evolution occurs in populations of reproducing individuals. The structure of the population affects the outcome of the evolutionary process. Evolutionary graph theory is a powerful approach to study this phenomenon. There are two graphs. The interaction graph specifies who interacts with whom for payoff in the context of evolution. The replacement graph specifies who competes with whom for reproduction. The vertices of the two graphs are the same, and each vertex corresponds to an individual of the population. The fitness (or the reproductive rate) is a non-negative number, and depends on the payoff. A key quantity is the fixation probability of a new mutant. It is defined as the probability that a newly introduced mutant (on a single vertex) generates a lineage of offspring which eventually takes over the entire population of resident individuals. The basic computational questions are as follows: (i) the qualitative question asks whether the fixation probability is positive; and (ii) the quantitative approximation question asks for an approximation of the fixation probability. Our main results are as follows: First, we consider a special case of the general problem, where the residents do not reproduce. We show that the qualitative question is NP-complete, and the quantitative approximation question is #P-complete, and the hardness results hold even in the special case where the interaction and the replacement graphs coincide. Second, we show that in general both the qualitative and the quantitative approximation questions are PSPACE-complete. The PSPACE-hardness result for quantitative approximation holds even when the fitness is always positive.' alternative_title: - IST Austria Technical Report author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Rasmus full_name: Ibsen-Jensen, Rasmus id: 3B699956-F248-11E8-B48F-1D18A9856A87 last_name: Ibsen-Jensen orcid: 0000-0003-4783-0389 - first_name: Martin full_name: Nowak, Martin last_name: Nowak citation: ama: Chatterjee K, Ibsen-Jensen R, Nowak M. The Complexity of Evolutionary Games on Graphs. IST Austria; 2015. doi:10.15479/AT:IST-2015-323-v2-2 apa: Chatterjee, K., Ibsen-Jensen, R., & Nowak, M. (2015). The complexity of evolutionary games on graphs. IST Austria. https://doi.org/10.15479/AT:IST-2015-323-v2-2 chicago: Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, and Martin Nowak. The Complexity of Evolutionary Games on Graphs. IST Austria, 2015. https://doi.org/10.15479/AT:IST-2015-323-v2-2. ieee: K. Chatterjee, R. Ibsen-Jensen, and M. Nowak, The complexity of evolutionary games on graphs. IST Austria, 2015. ista: Chatterjee K, Ibsen-Jensen R, Nowak M. 2015. The complexity of evolutionary games on graphs, IST Austria, 18p. mla: Chatterjee, Krishnendu, et al. The Complexity of Evolutionary Games on Graphs. IST Austria, 2015, doi:10.15479/AT:IST-2015-323-v2-2. short: K. Chatterjee, R. Ibsen-Jensen, M. Nowak, The Complexity of Evolutionary Games on Graphs, IST Austria, 2015. date_created: 2018-12-12T11:39:21Z date_published: 2015-06-16T00:00:00Z date_updated: 2023-02-23T12:26:10Z day: '16' ddc: - '005' - '576' department: - _id: KrCh doi: 10.15479/AT:IST-2015-323-v2-2 file: - access_level: open_access checksum: 66aace7d367032af97c15e35c9be9636 content_type: application/pdf creator: system date_created: 2018-12-12T11:53:23Z date_updated: 2020-07-14T12:46:56Z file_id: '5484' file_name: IST-2015-323-v2+2_main.pdf file_size: 466161 relation: main_file file_date_updated: 2020-07-14T12:46:56Z has_accepted_license: '1' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: '18' publication_identifier: issn: - 2664-1690 publication_status: published publisher: IST Austria pubrep_id: '338' related_material: record: - id: '5421' relation: earlier_version status: public - id: '5432' relation: earlier_version status: public status: public title: The complexity of evolutionary games on graphs type: technical_report user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2015' ...