The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform
Alexandra Silva - One of the best experts on this subject based on the ideXlab platform.
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MPC - Completeness and Incompleteness of Synchronous Kleene Algebra
Lecture Notes in Computer Science, 2019Co-Authors: Jana Wagemaker, Marcello M. Bonsangue, Tobias Kappé, Alexandra SilvaAbstract:Synchronous Kleene algebra (SKA), an extension of Kleene algebra (KA), was proposed by Prisacariu as a tool for reasoning about programs that may execute synchronously, i.e., in lock-step. We provide a countermodel witnessing that the axioms of SKA are incomplete w.r.t. its Language Semantics, by exploiting a lack of interaction between the synchronous product operator and the Kleene star. We then propose an alternative set of axioms for SKA, based on Salomaa’s axiomatisation of regular Languages, and show that these provide a sound and complete characterisation w.r.t. the original Language Semantics.
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Completeness and Incompleteness of Synchronous Kleene Algebra.
arXiv: Logic in Computer Science, 2019Co-Authors: Jana Wagemaker, Marcello M. Bonsangue, Tobias Kappé, Alexandra SilvaAbstract:Synchronous Kleene algebra (SKA), an extension of Kleene algebra (KA), was proposed by Prisacariu as a tool for reasoning about programs that may execute synchronously, i.e., in lock-step. We provide a countermodel witnessing that the axioms of SKA are incomplete w.r.t. its Language Semantics, by exploiting a lack of interaction between the synchronous product operator and the Kleene star. We then propose an alternative set of axioms for SKA, based on Salomaa's axiomatisation of regular Languages, and show that these provide a sound and complete characterisation w.r.t. the original Language Semantics.
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ICTAC - Convex Language Semantics for Nondeterministic Probabilistic Automata
Theoretical Aspects of Computing – ICTAC 2018, 2018Co-Authors: Gerco Van Heerdt, Joel Ouaknine, Alexandra SilvaAbstract:We explore Language Semantics for automata combining probabilistic and nondeterministic behaviors. We first show that there are precisely two natural Semantics for probabilistic automata with nondeterminism. For both choices, we show that these automata are strictly more expressive than deterministic probabilistic automata, and we prove that the problem of checking Language equivalence is undecidable by reduction from the threshold problem. However, we provide a discounted metric that can be computed to arbitrarily high precision.
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convex Language Semantics for nondeterministic probabilistic automata
arXiv: Formal Languages and Automata Theory, 2018Co-Authors: Gerco Van Heerdt, Joel Ouaknine, Alexandra SilvaAbstract:We explore Language Semantics for automata combining probabilistic and nondeterministic behavior. We first show that there are precisely two natural Semantics for probabilistic automata with nondeterminism. For both choices, we show that these automata are strictly more expressive than deterministic probabilistic automata, and we prove that the problem of checking Language equivalence is undecidable by reduction from the threshold problem. However, we provide a discounted metric that can be computed to arbitrarily high precision.
Noah D Goodman - One of the best experts on this subject based on the ideXlab platform.
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CogSci - How many kinds of reasoning? Inference, probability, and natural Language Semantics
Cognitive Science, 2020Co-Authors: Daniel Lassiter, Noah D GoodmanAbstract:How many kinds of reasoning? Inference, probability, and natural Language Semantics Daniel Lassiter, Noah D. Goodman Department of Psychology, Stanford University {danlassiter, ngoodman} @ stanford.edu Abstract lar, Rips and Heit & Rotello argue that non-linearities can- not be accounted for by probabilistic theories of reasoning, which identify the strength of an argument with the condi- tional probability of the conclusion given the premises (Heit, 1998; Kemp & Tenenbaum, 2009; Oaksford & Chater, 2007; Tenenbaum, Griffiths, & Kemp, 2006). On the other hand, they claim that the results are consistent with two-process the- ories of reasoning (Evans & Over, 1996). We argue that the manipulation involving “necessary” and “plausible” hinges not on a qualitative distinction between two reasoning processes, but rather on facts about the se- mantics of these words which can be modeled using a single underlying scale of argument strength—conditional probabil- ity. We propose a semantically motivated model of reasoning with epistemic concepts which predicts non-linear response patterns depending on the choice of modal similar to those observed in previous work, and makes detailed quantitative predictions about response patterns in invalid arguments. We test the claim that the modal word is the crucial factor using a new paradigm that isolates its effects. Our arguments had the same form as the examples above, except that we placed the modal word of interest in the conclusion: Previous research (Heit & Rotello, 2010; Rips, 2001; Rotello & Heit, 2009) has suggested that differences between inductive and deductive reasoning cannot be explained by probabilistic theories, and instead support two-process accounts of reason- ing. We provide a probabilistic model that predicts the ob- served non-linearities and makes quantitative predictions about responses as a function of argument strength. Predictions were tested using a novel experimental paradigm that elicits the previously-reported response patterns with a minimal manip- ulation, changing only one word between conditions. We also found a good fit with quantitative model predictions, indicating that a probabilistic theory of reasoning can account in a clear and parsimonious way for qualitative and quantitative data pre- viously argued to falsify them. We also relate our model to recent work in linguistics, arguing that careful attention to the Semantics of Language used to pose reasoning problems will sharpen the questions asked in the psychology of reasoning. Keywords: Reasoning, induction, deduction, probabilistic model, formal Semantics. Suppose that you have learned a new biological fact about mammals: whales and dogs both use enzyme B-32 to digest their food. Is it now necessary that horses do the same? Is it plausible, possible, or more likely than not? Expressions of this type—known as epistemic modals in linguistics— have played a crucial role in recent work that argues for a sharp qualitative distinction between inductive and deductive modes of reasoning. In the paradigm introduced by Rips (2001) and extended by Heit and Rotello (2010); Rotello and Heit (2009), participants are divided into two conditions and are either asked to judge whether a conclusion is “necessary” assuming that some premises are true, or whether it is “plau- sible”. The former is identified with the deductive mode of reasoning, and the latter with the inductive mode. These authors asked participants in both conditions to eval- uate a variety of logically valid and logically invalid ar- guments. An example invalid argument might be “Cows have sesamoid bones; Mice have sesamoid bones; therefore, Horses have sesamoid bones”. An example valid argument might be “Mammals have sesamoid bones; therefore, horses have sesamoid bones.” They found that there was a non-linear relationship between the endorsement rates of arguments de- pending on condition: participants in both conditions gener- ally endorsed logically valid arguments, but participants in the deductive condition were much less likely to endorse in- valid arguments than those in the inductive condition. These results are interpreted as a challenge to theories of reason- ing which rely on a single dimension of argument strength and interpret deductive validity as simply the upper extreme of this dimension(Harman, 1999; Johnson-Laird, 1994; Os- herson, Smith, Wilkie, Lopez, & Shafir, 1990). In particu- Premise 1: Cows have sesamoid bones. Premise 2: Mice have sesamoid bones. Conclusion: It is {plausible/necessary/possible/likely/ probable/certain} that horses have sesamoid bones. We will refer to configurations such as “It is plausi- ble/possible/etc. that C” as a modal frame. If varying the modal frame gives rise to a non-linear pattern of responses similar to the one found in previous work, this would indicate that an explanation of these results should be framed in terms of the meaning of these modal words. Together, the model and experimental evidence indicate that the negative conclusions of previous work regarding one- dimensional theories of argument strength are not warranted: it is possible to explain non-linear response patterns with a probabilistic account of argument strength. Previous Work Rips (2001) conducted a reasoning experiment designed to investigate the traditional distinction between deductive and inductive reasoning. Participants in two groups were asked to judge arguments either according to whether the conclu- sion was necessary (assuming that the premises were true) or whether it was plausible. Most participants in both conditions accepted logically valid arguments and rejected invalid argu- ments whose conclusion was not causally consistent with the
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how many kinds of reasoning inference probability and natural Language Semantics
Cognitive Science, 2012Co-Authors: Daniel Lassiter, Noah D GoodmanAbstract:How many kinds of reasoning? Inference, probability, and natural Language Semantics Daniel Lassiter, Noah D. Goodman Department of Psychology, Stanford University {danlassiter, ngoodman} @ stanford.edu Abstract lar, Rips and Heit & Rotello argue that non-linearities can- not be accounted for by probabilistic theories of reasoning, which identify the strength of an argument with the condi- tional probability of the conclusion given the premises (Heit, 1998; Kemp & Tenenbaum, 2009; Oaksford & Chater, 2007; Tenenbaum, Griffiths, & Kemp, 2006). On the other hand, they claim that the results are consistent with two-process the- ories of reasoning (Evans & Over, 1996). We argue that the manipulation involving “necessary” and “plausible” hinges not on a qualitative distinction between two reasoning processes, but rather on facts about the se- mantics of these words which can be modeled using a single underlying scale of argument strength—conditional probabil- ity. We propose a semantically motivated model of reasoning with epistemic concepts which predicts non-linear response patterns depending on the choice of modal similar to those observed in previous work, and makes detailed quantitative predictions about response patterns in invalid arguments. We test the claim that the modal word is the crucial factor using a new paradigm that isolates its effects. Our arguments had the same form as the examples above, except that we placed the modal word of interest in the conclusion: Previous research (Heit & Rotello, 2010; Rips, 2001; Rotello & Heit, 2009) has suggested that differences between inductive and deductive reasoning cannot be explained by probabilistic theories, and instead support two-process accounts of reason- ing. We provide a probabilistic model that predicts the ob- served non-linearities and makes quantitative predictions about responses as a function of argument strength. Predictions were tested using a novel experimental paradigm that elicits the previously-reported response patterns with a minimal manip- ulation, changing only one word between conditions. We also found a good fit with quantitative model predictions, indicating that a probabilistic theory of reasoning can account in a clear and parsimonious way for qualitative and quantitative data pre- viously argued to falsify them. We also relate our model to recent work in linguistics, arguing that careful attention to the Semantics of Language used to pose reasoning problems will sharpen the questions asked in the psychology of reasoning. Keywords: Reasoning, induction, deduction, probabilistic model, formal Semantics. Suppose that you have learned a new biological fact about mammals: whales and dogs both use enzyme B-32 to digest their food. Is it now necessary that horses do the same? Is it plausible, possible, or more likely than not? Expressions of this type—known as epistemic modals in linguistics— have played a crucial role in recent work that argues for a sharp qualitative distinction between inductive and deductive modes of reasoning. In the paradigm introduced by Rips (2001) and extended by Heit and Rotello (2010); Rotello and Heit (2009), participants are divided into two conditions and are either asked to judge whether a conclusion is “necessary” assuming that some premises are true, or whether it is “plau- sible”. The former is identified with the deductive mode of reasoning, and the latter with the inductive mode. These authors asked participants in both conditions to eval- uate a variety of logically valid and logically invalid ar- guments. An example invalid argument might be “Cows have sesamoid bones; Mice have sesamoid bones; therefore, Horses have sesamoid bones”. An example valid argument might be “Mammals have sesamoid bones; therefore, horses have sesamoid bones.” They found that there was a non-linear relationship between the endorsement rates of arguments de- pending on condition: participants in both conditions gener- ally endorsed logically valid arguments, but participants in the deductive condition were much less likely to endorse in- valid arguments than those in the inductive condition. These results are interpreted as a challenge to theories of reason- ing which rely on a single dimension of argument strength and interpret deductive validity as simply the upper extreme of this dimension(Harman, 1999; Johnson-Laird, 1994; Os- herson, Smith, Wilkie, Lopez, & Shafir, 1990). In particu- Premise 1: Cows have sesamoid bones. Premise 2: Mice have sesamoid bones. Conclusion: It is {plausible/necessary/possible/likely/ probable/certain} that horses have sesamoid bones. We will refer to configurations such as “It is plausi- ble/possible/etc. that C” as a modal frame. If varying the modal frame gives rise to a non-linear pattern of responses similar to the one found in previous work, this would indicate that an explanation of these results should be framed in terms of the meaning of these modal words. Together, the model and experimental evidence indicate that the negative conclusions of previous work regarding one- dimensional theories of argument strength are not warranted: it is possible to explain non-linear response patterns with a probabilistic account of argument strength. Previous Work Rips (2001) conducted a reasoning experiment designed to investigate the traditional distinction between deductive and inductive reasoning. Participants in two groups were asked to judge arguments either according to whether the conclu- sion was necessary (assuming that the premises were true) or whether it was plausible. Most participants in both conditions accepted logically valid arguments and rejected invalid argu- ments whose conclusion was not causally consistent with the
Daniel Lassiter - One of the best experts on this subject based on the ideXlab platform.
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CogSci - How many kinds of reasoning? Inference, probability, and natural Language Semantics
Cognitive Science, 2020Co-Authors: Daniel Lassiter, Noah D GoodmanAbstract:How many kinds of reasoning? Inference, probability, and natural Language Semantics Daniel Lassiter, Noah D. Goodman Department of Psychology, Stanford University {danlassiter, ngoodman} @ stanford.edu Abstract lar, Rips and Heit & Rotello argue that non-linearities can- not be accounted for by probabilistic theories of reasoning, which identify the strength of an argument with the condi- tional probability of the conclusion given the premises (Heit, 1998; Kemp & Tenenbaum, 2009; Oaksford & Chater, 2007; Tenenbaum, Griffiths, & Kemp, 2006). On the other hand, they claim that the results are consistent with two-process the- ories of reasoning (Evans & Over, 1996). We argue that the manipulation involving “necessary” and “plausible” hinges not on a qualitative distinction between two reasoning processes, but rather on facts about the se- mantics of these words which can be modeled using a single underlying scale of argument strength—conditional probabil- ity. We propose a semantically motivated model of reasoning with epistemic concepts which predicts non-linear response patterns depending on the choice of modal similar to those observed in previous work, and makes detailed quantitative predictions about response patterns in invalid arguments. We test the claim that the modal word is the crucial factor using a new paradigm that isolates its effects. Our arguments had the same form as the examples above, except that we placed the modal word of interest in the conclusion: Previous research (Heit & Rotello, 2010; Rips, 2001; Rotello & Heit, 2009) has suggested that differences between inductive and deductive reasoning cannot be explained by probabilistic theories, and instead support two-process accounts of reason- ing. We provide a probabilistic model that predicts the ob- served non-linearities and makes quantitative predictions about responses as a function of argument strength. Predictions were tested using a novel experimental paradigm that elicits the previously-reported response patterns with a minimal manip- ulation, changing only one word between conditions. We also found a good fit with quantitative model predictions, indicating that a probabilistic theory of reasoning can account in a clear and parsimonious way for qualitative and quantitative data pre- viously argued to falsify them. We also relate our model to recent work in linguistics, arguing that careful attention to the Semantics of Language used to pose reasoning problems will sharpen the questions asked in the psychology of reasoning. Keywords: Reasoning, induction, deduction, probabilistic model, formal Semantics. Suppose that you have learned a new biological fact about mammals: whales and dogs both use enzyme B-32 to digest their food. Is it now necessary that horses do the same? Is it plausible, possible, or more likely than not? Expressions of this type—known as epistemic modals in linguistics— have played a crucial role in recent work that argues for a sharp qualitative distinction between inductive and deductive modes of reasoning. In the paradigm introduced by Rips (2001) and extended by Heit and Rotello (2010); Rotello and Heit (2009), participants are divided into two conditions and are either asked to judge whether a conclusion is “necessary” assuming that some premises are true, or whether it is “plau- sible”. The former is identified with the deductive mode of reasoning, and the latter with the inductive mode. These authors asked participants in both conditions to eval- uate a variety of logically valid and logically invalid ar- guments. An example invalid argument might be “Cows have sesamoid bones; Mice have sesamoid bones; therefore, Horses have sesamoid bones”. An example valid argument might be “Mammals have sesamoid bones; therefore, horses have sesamoid bones.” They found that there was a non-linear relationship between the endorsement rates of arguments de- pending on condition: participants in both conditions gener- ally endorsed logically valid arguments, but participants in the deductive condition were much less likely to endorse in- valid arguments than those in the inductive condition. These results are interpreted as a challenge to theories of reason- ing which rely on a single dimension of argument strength and interpret deductive validity as simply the upper extreme of this dimension(Harman, 1999; Johnson-Laird, 1994; Os- herson, Smith, Wilkie, Lopez, & Shafir, 1990). In particu- Premise 1: Cows have sesamoid bones. Premise 2: Mice have sesamoid bones. Conclusion: It is {plausible/necessary/possible/likely/ probable/certain} that horses have sesamoid bones. We will refer to configurations such as “It is plausi- ble/possible/etc. that C” as a modal frame. If varying the modal frame gives rise to a non-linear pattern of responses similar to the one found in previous work, this would indicate that an explanation of these results should be framed in terms of the meaning of these modal words. Together, the model and experimental evidence indicate that the negative conclusions of previous work regarding one- dimensional theories of argument strength are not warranted: it is possible to explain non-linear response patterns with a probabilistic account of argument strength. Previous Work Rips (2001) conducted a reasoning experiment designed to investigate the traditional distinction between deductive and inductive reasoning. Participants in two groups were asked to judge arguments either according to whether the conclu- sion was necessary (assuming that the premises were true) or whether it was plausible. Most participants in both conditions accepted logically valid arguments and rejected invalid argu- ments whose conclusion was not causally consistent with the
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how many kinds of reasoning inference probability and natural Language Semantics
Cognitive Science, 2012Co-Authors: Daniel Lassiter, Noah D GoodmanAbstract:How many kinds of reasoning? Inference, probability, and natural Language Semantics Daniel Lassiter, Noah D. Goodman Department of Psychology, Stanford University {danlassiter, ngoodman} @ stanford.edu Abstract lar, Rips and Heit & Rotello argue that non-linearities can- not be accounted for by probabilistic theories of reasoning, which identify the strength of an argument with the condi- tional probability of the conclusion given the premises (Heit, 1998; Kemp & Tenenbaum, 2009; Oaksford & Chater, 2007; Tenenbaum, Griffiths, & Kemp, 2006). On the other hand, they claim that the results are consistent with two-process the- ories of reasoning (Evans & Over, 1996). We argue that the manipulation involving “necessary” and “plausible” hinges not on a qualitative distinction between two reasoning processes, but rather on facts about the se- mantics of these words which can be modeled using a single underlying scale of argument strength—conditional probabil- ity. We propose a semantically motivated model of reasoning with epistemic concepts which predicts non-linear response patterns depending on the choice of modal similar to those observed in previous work, and makes detailed quantitative predictions about response patterns in invalid arguments. We test the claim that the modal word is the crucial factor using a new paradigm that isolates its effects. Our arguments had the same form as the examples above, except that we placed the modal word of interest in the conclusion: Previous research (Heit & Rotello, 2010; Rips, 2001; Rotello & Heit, 2009) has suggested that differences between inductive and deductive reasoning cannot be explained by probabilistic theories, and instead support two-process accounts of reason- ing. We provide a probabilistic model that predicts the ob- served non-linearities and makes quantitative predictions about responses as a function of argument strength. Predictions were tested using a novel experimental paradigm that elicits the previously-reported response patterns with a minimal manip- ulation, changing only one word between conditions. We also found a good fit with quantitative model predictions, indicating that a probabilistic theory of reasoning can account in a clear and parsimonious way for qualitative and quantitative data pre- viously argued to falsify them. We also relate our model to recent work in linguistics, arguing that careful attention to the Semantics of Language used to pose reasoning problems will sharpen the questions asked in the psychology of reasoning. Keywords: Reasoning, induction, deduction, probabilistic model, formal Semantics. Suppose that you have learned a new biological fact about mammals: whales and dogs both use enzyme B-32 to digest their food. Is it now necessary that horses do the same? Is it plausible, possible, or more likely than not? Expressions of this type—known as epistemic modals in linguistics— have played a crucial role in recent work that argues for a sharp qualitative distinction between inductive and deductive modes of reasoning. In the paradigm introduced by Rips (2001) and extended by Heit and Rotello (2010); Rotello and Heit (2009), participants are divided into two conditions and are either asked to judge whether a conclusion is “necessary” assuming that some premises are true, or whether it is “plau- sible”. The former is identified with the deductive mode of reasoning, and the latter with the inductive mode. These authors asked participants in both conditions to eval- uate a variety of logically valid and logically invalid ar- guments. An example invalid argument might be “Cows have sesamoid bones; Mice have sesamoid bones; therefore, Horses have sesamoid bones”. An example valid argument might be “Mammals have sesamoid bones; therefore, horses have sesamoid bones.” They found that there was a non-linear relationship between the endorsement rates of arguments de- pending on condition: participants in both conditions gener- ally endorsed logically valid arguments, but participants in the deductive condition were much less likely to endorse in- valid arguments than those in the inductive condition. These results are interpreted as a challenge to theories of reason- ing which rely on a single dimension of argument strength and interpret deductive validity as simply the upper extreme of this dimension(Harman, 1999; Johnson-Laird, 1994; Os- herson, Smith, Wilkie, Lopez, & Shafir, 1990). In particu- Premise 1: Cows have sesamoid bones. Premise 2: Mice have sesamoid bones. Conclusion: It is {plausible/necessary/possible/likely/ probable/certain} that horses have sesamoid bones. We will refer to configurations such as “It is plausi- ble/possible/etc. that C” as a modal frame. If varying the modal frame gives rise to a non-linear pattern of responses similar to the one found in previous work, this would indicate that an explanation of these results should be framed in terms of the meaning of these modal words. Together, the model and experimental evidence indicate that the negative conclusions of previous work regarding one- dimensional theories of argument strength are not warranted: it is possible to explain non-linear response patterns with a probabilistic account of argument strength. Previous Work Rips (2001) conducted a reasoning experiment designed to investigate the traditional distinction between deductive and inductive reasoning. Participants in two groups were asked to judge arguments either according to whether the conclu- sion was necessary (assuming that the premises were true) or whether it was plausible. Most participants in both conditions accepted logically valid arguments and rejected invalid argu- ments whose conclusion was not causally consistent with the
Joel Ouaknine - One of the best experts on this subject based on the ideXlab platform.
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ICTAC - Convex Language Semantics for Nondeterministic Probabilistic Automata
Theoretical Aspects of Computing – ICTAC 2018, 2018Co-Authors: Gerco Van Heerdt, Joel Ouaknine, Alexandra SilvaAbstract:We explore Language Semantics for automata combining probabilistic and nondeterministic behaviors. We first show that there are precisely two natural Semantics for probabilistic automata with nondeterminism. For both choices, we show that these automata are strictly more expressive than deterministic probabilistic automata, and we prove that the problem of checking Language equivalence is undecidable by reduction from the threshold problem. However, we provide a discounted metric that can be computed to arbitrarily high precision.
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convex Language Semantics for nondeterministic probabilistic automata
arXiv: Formal Languages and Automata Theory, 2018Co-Authors: Gerco Van Heerdt, Joel Ouaknine, Alexandra SilvaAbstract:We explore Language Semantics for automata combining probabilistic and nondeterministic behavior. We first show that there are precisely two natural Semantics for probabilistic automata with nondeterminism. For both choices, we show that these automata are strictly more expressive than deterministic probabilistic automata, and we prove that the problem of checking Language equivalence is undecidable by reduction from the threshold problem. However, we provide a discounted metric that can be computed to arbitrarily high precision.
Gerco Van Heerdt - One of the best experts on this subject based on the ideXlab platform.
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ICTAC - Convex Language Semantics for Nondeterministic Probabilistic Automata
Theoretical Aspects of Computing – ICTAC 2018, 2018Co-Authors: Gerco Van Heerdt, Joel Ouaknine, Alexandra SilvaAbstract:We explore Language Semantics for automata combining probabilistic and nondeterministic behaviors. We first show that there are precisely two natural Semantics for probabilistic automata with nondeterminism. For both choices, we show that these automata are strictly more expressive than deterministic probabilistic automata, and we prove that the problem of checking Language equivalence is undecidable by reduction from the threshold problem. However, we provide a discounted metric that can be computed to arbitrarily high precision.
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convex Language Semantics for nondeterministic probabilistic automata
arXiv: Formal Languages and Automata Theory, 2018Co-Authors: Gerco Van Heerdt, Joel Ouaknine, Alexandra SilvaAbstract:We explore Language Semantics for automata combining probabilistic and nondeterministic behavior. We first show that there are precisely two natural Semantics for probabilistic automata with nondeterminism. For both choices, we show that these automata are strictly more expressive than deterministic probabilistic automata, and we prove that the problem of checking Language equivalence is undecidable by reduction from the threshold problem. However, we provide a discounted metric that can be computed to arbitrarily high precision.
