[{"month":"07","publication_identifier":{"eisbn":["978-1-4799-8875-4 "],"issn":["1043-6871 "]},"oa":1,"quality_controlled":"1","project":[{"name":"Quantitative Reactive Modeling","call_identifier":"FP7","_id":"25EE3708-B435-11E9-9278-68D0E5697425","grant_number":"267989"},{"name":"Rigorous Systems Engineering","call_identifier":"FWF","_id":"25832EC2-B435-11E9-9278-68D0E5697425","grant_number":"S 11407_N23"},{"grant_number":"Z211","_id":"25F42A32-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","call_identifier":"FWF"}],"conference":{"start_date":"2015-007-06","location":"Kyoto, Japan","end_date":"2015-07-10","name":"LICS: Logic in Computer Science"},"doi":"10.1109/LICS.2015.74","language":[{"iso":"eng"}],"file_date_updated":"2020-07-14T12:45:10Z","ec_funded":1,"publist_id":"5491","year":"2015","acknowledgement":"A technical report of the article is available at: https://research-explorer.app.ist.ac.at/record/5439","publication_status":"published","publisher":"IEEE","department":[{"_id":"ToHe"}],"author":[{"full_name":"Boker, Udi","id":"31E297B6-F248-11E8-B48F-1D18A9856A87","first_name":"Udi","last_name":"Boker"},{"first_name":"Thomas A","last_name":"Henzinger","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","orcid":"0000−0002−2985−7724","full_name":"Henzinger, Thomas A"},{"id":"2FC5DA74-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Otop","full_name":"Otop, Jan"}],"related_material":{"record":[{"id":"5439","status":"public","relation":"earlier_version"}]},"date_updated":"2023-02-23T12:26:27Z","date_created":"2018-12-11T11:53:19Z","scopus_import":1,"series_title":"Logic in Computer Science","day":"01","has_accepted_license":"1","article_processing_charge":"No","publication":"LICS","citation":{"short":"U. Boker, T.A. Henzinger, J. Otop, in:, LICS, IEEE, 2015, pp. 750–761.","mla":"Boker, Udi, et al. “The Target Discounted-Sum Problem.” LICS, IEEE, 2015, pp. 750–61, doi:10.1109/LICS.2015.74.","chicago":"Boker, Udi, Thomas A Henzinger, and Jan Otop. “The Target Discounted-Sum Problem.” In LICS, 750–61. Logic in Computer Science. IEEE, 2015. https://doi.org/10.1109/LICS.2015.74.","ama":"Boker U, Henzinger TA, Otop J. The target discounted-sum problem. In: LICS. Logic in Computer Science. IEEE; 2015:750-761. doi:10.1109/LICS.2015.74","apa":"Boker, U., Henzinger, T. A., & Otop, J. (2015). The target discounted-sum problem. In LICS (pp. 750–761). Kyoto, Japan: IEEE. https://doi.org/10.1109/LICS.2015.74","ieee":"U. Boker, T. A. Henzinger, and J. Otop, “The target discounted-sum problem,” in LICS, Kyoto, Japan, 2015, pp. 750–761.","ista":"Boker U, Henzinger TA, Otop J. 2015. The target discounted-sum problem. LICS. LICS: Logic in Computer ScienceLogic in Computer Science, 750–761."},"page":"750 - 761","date_published":"2015-07-01T00:00:00Z","type":"conference","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."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1659","ddc":["000"],"title":"The target discounted-sum problem","status":"public","oa_version":"Submitted Version","file":[{"relation":"main_file","file_id":"7852","checksum":"6abebca9c1a620e9e103a8f9222befac","date_updated":"2020-07-14T12:45:10Z","date_created":"2020-05-15T08:53:29Z","access_level":"open_access","file_name":"2015_LICS_Boker.pdf","content_type":"application/pdf","file_size":340215,"creator":"dernst"}]},{"date_published":"2015-07-01T00:00:00Z","citation":{"mla":"Chatterjee, Krishnendu, et al. “Edit Distance for Pushdown Automata.” 42nd International Colloquium, vol. 9135, no. Part II, Springer Nature, 2015, pp. 121–33, doi:10.1007/978-3-662-47666-6_10.","short":"K. Chatterjee, T.A. Henzinger, R. Ibsen-Jensen, J. Otop, in:, 42nd International Colloquium, Springer Nature, 2015, pp. 121–133.","chicago":"Chatterjee, Krishnendu, Thomas A Henzinger, Rasmus Ibsen-Jensen, and Jan Otop. “Edit Distance for Pushdown Automata.” In 42nd International Colloquium, 9135:121–33. Springer Nature, 2015. https://doi.org/10.1007/978-3-662-47666-6_10.","ama":"Chatterjee K, Henzinger TA, Ibsen-Jensen R, Otop J. Edit distance for pushdown automata. In: 42nd International Colloquium. Vol 9135. Springer Nature; 2015:121-133. doi:10.1007/978-3-662-47666-6_10","ista":"Chatterjee K, Henzinger TA, Ibsen-Jensen R, Otop J. 2015. Edit distance for pushdown automata. 42nd International Colloquium. ICALP: Automata, Languages and Programming, LNCS, vol. 9135, 121–133.","ieee":"K. Chatterjee, T. A. Henzinger, R. Ibsen-Jensen, and J. Otop, “Edit distance for pushdown automata,” in 42nd International Colloquium, Kyoto, Japan, 2015, vol. 9135, no. Part II, pp. 121–133.","apa":"Chatterjee, K., Henzinger, T. A., Ibsen-Jensen, R., & Otop, J. (2015). Edit distance for pushdown automata. In 42nd International Colloquium (Vol. 9135, pp. 121–133). Kyoto, Japan: Springer Nature. https://doi.org/10.1007/978-3-662-47666-6_10"},"publication":"42nd International Colloquium","page":"121 - 133","article_processing_charge":"No","day":"01","scopus_import":"1","pubrep_id":"321","oa_version":"None","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","_id":"1610","intvolume":" 9135","title":"Edit distance for pushdown automata","status":"public","issue":"Part II","abstract":[{"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. The problem of computing edit distance to pushdown automata 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.","lang":"eng"}],"type":"conference","alternative_title":["LNCS"],"doi":"10.1007/978-3-662-47666-6_10","conference":{"start_date":"2015-07-06","location":"Kyoto, Japan","end_date":"2015-07-10","name":"ICALP: Automata, Languages and Programming"},"language":[{"iso":"eng"}],"external_id":{"arxiv":["1504.08259"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1504.08259"}],"project":[{"name":"Quantitative Reactive Modeling","call_identifier":"FP7","grant_number":"267989","_id":"25EE3708-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","name":"The Wittgenstein Prize","grant_number":"Z211","_id":"25F42A32-B435-11E9-9278-68D0E5697425"},{"name":"Modern Graph Algorithmic Techniques in Formal Verification","call_identifier":"FWF","grant_number":"P 23499-N23","_id":"2584A770-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","name":"Game Theory","grant_number":"S11407","_id":"25863FF4-B435-11E9-9278-68D0E5697425"},{"name":"Quantitative Graph Games: Theory and Applications","call_identifier":"FP7","grant_number":"279307","_id":"2581B60A-B435-11E9-9278-68D0E5697425"},{"name":"Microsoft Research Faculty Fellowship","_id":"2587B514-B435-11E9-9278-68D0E5697425"},{"_id":"25832EC2-B435-11E9-9278-68D0E5697425","grant_number":"S 11407_N23","name":"Rigorous Systems Engineering","call_identifier":"FWF"}],"quality_controlled":"1","publication_identifier":{"isbn":["978-3-662-47665-9"]},"month":"07","related_material":{"record":[{"id":"465","status":"public","relation":"later_version"},{"id":"5438","relation":"earlier_version","status":"public"}]},"author":[{"full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X"},{"last_name":"Henzinger","first_name":"Thomas A","orcid":"0000−0002−2985−7724","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","full_name":"Henzinger, Thomas A"},{"full_name":"Ibsen-Jensen, Rasmus","last_name":"Ibsen-Jensen","first_name":"Rasmus","orcid":"0000-0003-4783-0389","id":"3B699956-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Otop, Jan","id":"2FC5DA74-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Otop"}],"volume":9135,"date_updated":"2023-02-23T12:26:24Z","date_created":"2018-12-11T11:53:01Z","year":"2015","department":[{"_id":"KrCh"},{"_id":"ToHe"}],"publisher":"Springer Nature","publication_status":"published","ec_funded":1,"publist_id":"5556"},{"publication_identifier":{"issn":["2664-1690"]},"has_accepted_license":"1","month":"04","day":"27","language":[{"iso":"eng"}],"date_published":"2015-04-27T00:00:00Z","doi":"10.15479/AT:IST-2015-330-v2-1","page":"27","oa":1,"citation":{"ista":"Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. 2015. Faster algorithms for quantitative verification in constant treewidth graphs, IST Austria, 27p.","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","ieee":"K. Chatterjee, R. Ibsen-Jensen, and A. Pavlogiannis, Faster algorithms for quantitative verification in constant treewidth graphs. IST Austria, 2015.","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","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.","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."},"abstract":[{"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. 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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.","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.","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","ista":"Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. 2015. Faster algorithms for quantitative verification in constant treewidth graphs, IST Austria, 31p.","ieee":"K. Chatterjee, R. Ibsen-Jensen, and A. Pavlogiannis, Faster algorithms for quantitative verification in constant treewidth graphs. IST Austria, 2015.","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"},"page":"31","date_published":"2015-02-10T00:00:00Z","doi":"10.15479/AT:IST-2015-319-v1-1","language":[{"iso":"eng"}],"type":"technical_report","alternative_title":["IST Austria Technical Report"],"file_date_updated":"2020-07-14T12:46:52Z","abstract":[{"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.","lang":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"5430","year":"2015","department":[{"_id":"KrCh"}],"publisher":"IST Austria","ddc":["000"],"title":"Faster algorithms for quantitative verification in constant treewidth graphs","status":"public","publication_status":"published","pubrep_id":"319","related_material":{"record":[{"id":"1607","relation":"later_version","status":"public"},{"status":"public","relation":"later_version","id":"5437"}]},"author":[{"full_name":"Chatterjee, Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X","first_name":"Krishnendu","last_name":"Chatterjee"},{"full_name":"Ibsen-Jensen, Rasmus","first_name":"Rasmus","last_name":"Ibsen-Jensen","id":"3B699956-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-4783-0389"},{"full_name":"Pavlogiannis, Andreas","orcid":"0000-0002-8943-0722","id":"49704004-F248-11E8-B48F-1D18A9856A87","last_name":"Pavlogiannis","first_name":"Andreas"}],"oa_version":"Published Version","file":[{"access_level":"open_access","file_name":"IST-2015-319-v1+1_long.pdf","file_size":1089651,"content_type":"application/pdf","creator":"system","relation":"main_file","file_id":"5482","checksum":"62c6ea01e342553dcafb88a070fb1ad5","date_updated":"2020-07-14T12:46:52Z","date_created":"2018-12-12T11:53:21Z"}],"date_updated":"2023-02-23T12:26:22Z","date_created":"2018-12-12T11:39:17Z"},{"has_accepted_license":"1","publication_identifier":{"issn":["2664-1690"]},"day":"18","month":"05","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","ieee":"U. Boker, T. A. Henzinger, and J. Otop, The target discounted-sum problem. IST Austria, 2015.","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","ista":"Boker U, Henzinger TA, Otop J. 2015. The target discounted-sum problem, IST Austria, 20p.","short":"U. Boker, T.A. Henzinger, J. Otop, The Target Discounted-Sum Problem, IST Austria, 2015.","mla":"Boker, Udi, et al. The Target Discounted-Sum Problem. IST Austria, 2015, doi: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."},"oa":1,"page":"20","date_published":"2015-05-18T00:00:00Z","doi":"10.15479/AT:IST-2015-335-v1-1","language":[{"iso":"eng"}],"type":"technical_report","alternative_title":["IST Austria Technical Report"],"file_date_updated":"2020-07-14T12:46:55Z","abstract":[{"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. 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