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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
*

We propose a

doi:10.1609/aaai.v33i01.33016179
fatcat:p3ezsotrtjay3hhsk6zimjhwqa
*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 P*µ*TL. 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) . ...##
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Tractable Probabilistic mu-Calculus That Expresses Probabilistic Temporal Logics

2015
*
Symposium on Theoretical Aspects of Computer Science
*

We revisit a recently introduced

doi:10.4230/lipics.stacs.2015.211
dblp:conf/stacs/CastroKP15
fatcat:whgrktaxbrf3lir3tqrunw7ur4
*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. ...##
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Equivalence of Probabilistic $$\mu $$ -Calculus and p-Automata
[chapter]

2017
*
Lecture Notes in Computer Science
*

Here, we show that the

doi:10.1007/978-3-319-60134-2_6
fatcat:4wp4flajcnhq7ohyy7ywdq3qxa
*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. ...##
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Reasoning About States of Probabilistic Sequential Programs
[chapter]

2006
*
Lecture Notes in Computer Science
*

The state logic is then used to obtain a sound Hoare-style

doi:10.1007/11874683_16
fatcat:ri4vxmijhvhalh4rggozysthc4
*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*. ...##
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Probabilistic asynchronous pi-calculus
[article]

2001
*
arXiv
*
pre-print

Finally, we show an implementation of the

arXiv:cs/0109002v1
fatcat:kzd6g2lp7rf73dusfisn5wsoqq
*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)! ...##
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Game-Based Local Model Checking for the Coalgebraic mu-Calculus

2019
*
International Conference on Concurrency Theory
*

, the monotone

doi:10.4230/lipics.concur.2019.35
dblp:conf/concur/HausmannS19
fatcat:2b4524tktjchhkr3v2aybi6qq4
*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. ...##
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Quasipolynomial Computation of Nested Fixpoints
[article]

2020
*
arXiv
*
pre-print

For instance, the model checking problems for the energy

arXiv:1907.07020v4
fatcat:k6rhwkj3pbdndp5dffscpaisdu
*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 ...##
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Reasoning about probabilistic sequential programs

2007
*
Theoretical Computer Science
*

A complete and decidable Hoare-style

doi:10.1016/j.tcs.2007.02.040
fatcat:tzpnm45kuzar7irg2y3vy4zanq
*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. ...##
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Quasipolynomial Computation of Nested Fixpoints
[chapter]

2021
*
Lecture Notes in Computer Science
*

For instance, the model checking problems for the energy $$\mu $$

doi:10.1007/978-3-030-72016-2_3
fatcat:up2kucajgbdj5nkkrrkxwq5sqa
*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*. ...##
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Optimal Satisfiability Checking for Arithmetic $$\mu $$ -Calculi
[chapter]

2019
*
Green Chemistry and Sustainable Technology
*

), as well as an extension of the (two-valued)

doi:10.1007/978-3-030-17127-8_16
dblp:conf/fossacs/HausmannS19
fatcat:a532tjzygzez5ctwmsohietthu
*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] . ...##
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Games, Probability, and the Quantitative μ-Calculus qMμ
[chapter]

2002
*
Lecture Notes in Computer Science
*

that to

doi:10.1007/3-540-36078-6_20
fatcat:4y7mtcvm6jbn7ledxfwunctoum
*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 qM*µ*extends ... Conclusion Our main contribution has been to introduce a novel game-based interpretation for the quantitative*µ*-*calculus*qM*µ*over*probabilistic*/angelic/demonic transition systems,*probabilistically*generalising ...##
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Optimal Satisfiability Checking for Arithmetic μ-Calculi
[article]

2019
*
arXiv
*
pre-print

)

arXiv:1901.04893v1
fatcat:kd5upgd6avev3kdofjxpab4y6y
*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] . ...##
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Expressiveness of Probabilistic π-calculus

2006
*
Electronical Notes in Theoretical Computer Science
*

In this work we propose a

doi:10.1016/j.entcs.2006.07.015
fatcat:wn3wgoqc4bej3on6ujmyatcjtq
*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*. ...##
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Characterising Probabilistic Alternating Simulation for Concurrent Games

2020
*
2020 International Symposium on Theoretical Aspects of Software Engineering (TASE)
*

*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 ...

##
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Characterising Probabilistic Alternating Simulation for Concurrent Games
[article]

2019
*
arXiv
*
pre-print

*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 | ...

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