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Probabilistic Alternating-Time µ-Calculus
2019
PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE
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We propose a probabilistic extension of Alternating µ-Calculus (AMC), named PAMC, for reasoning about strategic abilities of agents in stochastic multi-agent systems. ...
PAMC subsumes existing logics AMC and PµTL. The usefulness of PAMC is exemplified by applications in genetic regulatory networks. ...
Probabilistic Alternating-Time µ-Calculus Probabilistic alternating-time µ-calculus is a simple and succinct, but natural, probabilistic extension of AMC (Alur, Henzinger, and Kupferman 2002) . ...
doi:10.1609/aaai.v33i01.33016179
fatcat:p3ezsotrtjay3hhsk6zimjhwqa
Tractable Probabilistic mu-Calculus That Expresses Probabilistic Temporal Logics
2015
Symposium on Theoretical Aspects of Computer Science
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We revisit a recently introduced probabilistic µ-calculus and study an expressive fragment of it. ...
An important feature of this extended version of pctl is that its model checking is only exponential w.r.t. the alternation depth of fixed points, one of the main characteristics of Kozen's µ-calculus. ...
A Probabilistic µ-Calculus In this section we present our version of probabilistic µ-calculus (denoted µ p -calculus). Unlike the "normal" µ-calculus, µ p -calculus is two sorted. ...
doi:10.4230/lipics.stacs.2015.211
dblp:conf/stacs/CastroKP15
fatcat:whgrktaxbrf3lir3tqrunw7ur4
Equivalence of Probabilistic $$\mu $$ -Calculus and p-Automata
[chapter]
2017
Lecture Notes in Computer Science
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Here, we show that the probabilistic µ-calculus µ p -calculus and p-automata (parity alternating Markov chain automata) have an equally strong connection. ...
An important characteristic of Kozen's µ-calculus is its strong connection with parity alternating tree automata. ...
Conclusion The aim of this paper was to investigate the connection between µ p -calculus and p-automata and to assess their equivalence in expressive power. ...
doi:10.1007/978-3-319-60134-2_6
fatcat:4wp4flajcnhq7ohyy7ywdq3qxa
Reasoning About States of Probabilistic Sequential Programs
[chapter]
2006
Lecture Notes in Computer Science
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The state logic is then used to obtain a sound Hoare-style calculus for basic probabilistic sequential programs. ...
The Hoare calculus presented herein is the first probabilistic Hoare calculus with a complete and decidable state logic that has truth-functional propositional (not arithmetical) connectives. ...
We can prove the security of the one-time pad in our calculus. ...
doi:10.1007/11874683_16
fatcat:ri4vxmijhvhalh4rggozysthc4
Probabilistic asynchronous pi-calculus
[article]
2001
arXiv
pre-print
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Finally, we show an implementation of the probabilistic asynchronous pi-calculus in a Java-like language. ...
We propose an extension of the asynchronous pi-calculus with a notion of random choice. ...
The probability that an execution contains n − 1 draws where the alternation is violated k times is therefore 1 2 n−2 (n − 2)! k!(n − 2 − k)! ...
arXiv:cs/0109002v1
fatcat:kzd6g2lp7rf73dusfisn5wsoqq
Game-Based Local Model Checking for the Coalgebraic mu-Calculus
2019
International Conference on Concurrency Theory
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, the monotone µ-calculus, the probabilistic µ-calculus, and the alternating-time µ-calculus. ...
This applies in particular to the monotone µ-calculus, the alternating-time µ-calculus, and the graded µ-calculus with grades coded in unary. ...
Alternating-time µ-calculus: Fix a set N = {1, . . . , n} of agents. ...
doi:10.4230/lipics.concur.2019.35
dblp:conf/concur/HausmannS19
fatcat:2b4524tktjchhkr3v2aybi6qq4
Quasipolynomial Computation of Nested Fixpoints
[article]
2020
arXiv
pre-print
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For instance, the model checking problems for the energy μ-calculus, finite latticed μ-calculi, and the graded and the (two-valued) probabilistic μ-calculus – with numbers coded in binary – can be solved ...
μ-calculi is in QP. ...
probabilistic µ-calculus (e.g ...
arXiv:1907.07020v4
fatcat:k6rhwkj3pbdndp5dffscpaisdu
Reasoning about probabilistic sequential programs
2007
Theoretical Computer Science
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A complete and decidable Hoare-style calculus for iteration-free probabilistic sequential programs is presented using a state logic with truth-functional propositional (not arithmetical) connectives. 143 ...
η is satisfied by a (sub)probability measure µ on valuations over the memory cell if µ(v) is non-zero only when the valuation v satisfies γ and there is a valuation µ such that µ + µ satisfies η. ...
One-time pad. A one-time pad is a provably secure way of encrypting a bit-string. ...
doi:10.1016/j.tcs.2007.02.040
fatcat:tzpnm45kuzar7irg2y3vy4zanq
Quasipolynomial Computation of Nested Fixpoints
[chapter]
2021
Lecture Notes in Computer Science
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For instance, the model checking problems for the energy $$\mu $$ μ -calculus, finite latticed $$\mu $$ μ -calculi, and the graded and the (two-valued) probabilistic $$\mu $$ μ -calculus – with numbers ...
that model checking for these $$\mu $$ μ -calculi is in $$\textsc {QP}$$ QP . ...
for satisfiability checking in the graded μ-calculus, the probabilistic μ-calculus, the monotone μ-calculus, and the alternating-time μ-calculus. ...
doi:10.1007/978-3-030-72016-2_3
fatcat:up2kucajgbdj5nkkrrkxwq5sqa
Optimal Satisfiability Checking for Arithmetic $$\mu $$ -Calculi
[chapter]
2019
Green Chemistry and Sustainable Technology
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), as well as an extension of the (two-valued) probabilistic µ-calculus with polynomial inequalities. ...
The coalgebraic µ-calculus provides a generic semantic framework for fixpoint logics with branching types beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. ...
, 24] , the alternating-time μ-calculus [1] , and the monotone μ-calculus, which contains Parikh's game logic [28] . ...
doi:10.1007/978-3-030-17127-8_16
dblp:conf/fossacs/HausmannS19
fatcat:a532tjzygzez5ctwmsohietthu
Games, Probability, and the Quantitative μ-Calculus qMμ
[chapter]
2002
Lecture Notes in Computer Science
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that to probabilistic choice. ...
The µ-calculus is a powerful tool for specifying and verifying transition systems, including those with demonic (universal) and angelic (existential) choice; its quantitative generalisation qMµ extends ...
Conclusion Our main contribution has been to introduce a novel game-based interpretation for the quantitative µ-calculus qMµ over probabilistic/angelic/demonic transition systems, probabilistically generalising ...
doi:10.1007/3-540-36078-6_20
fatcat:4y7mtcvm6jbn7ledxfwunctoum
Optimal Satisfiability Checking for Arithmetic μ-Calculi
[article]
2019
arXiv
pre-print
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) probabilistic μ-calculus with polynomial inequalities. ...
The coalgebraic μ-calculus provides a generic semantic framework for fixpoint logics with branching types beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. ...
, 23] , the alternating-time µ-calculus [1] , and the monotone µ-calculus, which contains Parikh's game logic [26] . ...
arXiv:1901.04893v1
fatcat:kd5upgd6avev3kdofjxpab4y6y
Expressiveness of Probabilistic π-calculus
2006
Electronical Notes in Theoretical Computer Science
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In this work we propose a probabilistic extension of the π-calculus. ...
We develop the operational semantics of this calculus, and then we investigate its expressiveness. ...
This is because the alternative between these three cases should be nondeterministic rather than probabilistic, as in the classical π-calculus. ...
doi:10.1016/j.entcs.2006.07.015
fatcat:wn3wgoqc4bej3on6ujmyatcjtq
Characterising Probabilistic Alternating Simulation for Concurrent Games
2020
2020 International Symposium on Theoretical Aspects of Software Engineering (TASE)
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Probabilistic alternating simulation is an important tool to compare the behaviour of different probabilistic game structures. ...
Probabilistic game structures combine both nondeterminism and stochasticity, where players repeatedly take actions simultaneously to move to the next state of the concurrent game. ...
This logic is then extended with variables and fixpoint operators, resulting in a Probabilistic Alternating-time µ-calculus (PAMu), and the logic characterisation of probabilistic alternating simulation ...
doi:10.1109/tase49443.2020.00025
fatcat:zeupptk65vd3vgte3bwtchrdne
Characterising Probabilistic Alternating Simulation for Concurrent Games
[article]
2019
arXiv
pre-print
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Probabilistic alternating simulation is an important tool to compare the behaviour of different probabilistic game structures. ...
In this paper, we present a sound and complete modal characterisation of this simulation relation by proposing a new logic based on probabilistic distributions. ...
In this section, we extend the logic L ⊕ into a Probabilistic Alternating-time µ-calculus (PAMu), by adding variables and fixpoint operators. ϕ ::= p | ¬p | i∈I ϕi | i∈I ϕi | I ϕ | j∈J ϕj | j∈J pjϕj | ...
arXiv:1907.03928v1
fatcat:jkc6jzuvcjdr3epqf2ay46fsqy
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