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Volumn 3, Issue , 2007, Pages 721-756

12 Modal mu-calculi

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EID: 40949090581     PISSN: 15702464     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1570-2464(07)80015-2     Document Type: Article
Times cited : (136)

References (70)
  • 2
    • 0033295153 scopus 로고    scopus 로고
    • Theμ-calculus alternation hierarchy is strict on binary trees
    • Arnold A. Theμ-calculus alternation hierarchy is strict on binary trees. Theoretical Informatics and Applications 33 4/5 (1999) 329-340
    • (1999) Theoretical Informatics and Applications , vol.33 , Issue.4-5 , pp. 329-340
    • Arnold, A.1
  • 3
    • 0342373345 scopus 로고
    • Fixed point characterization of Biichi automata on infinite trees
    • Arnold A., and Niwinski D. Fixed point characterization of Biichi automata on infinite trees. J. Inf. Process. Cybern. EIK 26 (1990) 451-459
    • (1990) J. Inf. Process. Cybern. EIK , vol.26 , pp. 451-459
    • Arnold, A.1    Niwinski, D.2
  • 4
    • 0038103635 scopus 로고    scopus 로고
    • Rudiments of μ-Calculus
    • North-Holland Vol. 146
    • Arnold A., and Niwinski D. Rudiments of μ-Calculus. Studies in Logic (2001), North-Holland Vol. 146
    • (2001) Studies in Logic
    • Arnold, A.1    Niwinski, D.2
  • 5
    • 0029716738 scopus 로고    scopus 로고
    • Efficient model checking via the equational mu-calculus
    • Bhat G., and Cleaveland R. Efficient model checking via the equational mu-calculus. Proc. LICS '96 (1996) 304-312
    • (1996) Proc. LICS '96 , pp. 304-312
    • Bhat, G.1    Cleaveland, R.2
  • 7
    • 40949103904 scopus 로고    scopus 로고
    • The modal mu-calculus alternation hierarchy is strict
    • Bradfield J.C. The modal mu-calculus alternation hierarchy is strict. Theor. Comput. Sci. 195 (1996) 4-312
    • (1996) Theor. Comput. Sci. , Issue.195 , pp. 4-312
    • Bradfield, J.C.1
  • 8
    • 78649870647 scopus 로고    scopus 로고
    • Simplifying the modal mu-calculus alternation hierarchy
    • Bradfield J.C. Simplifying the modal mu-calculus alternation hierarchy. Proc. STAGS 98 LNCS 1373 (1998) 39-49
    • (1998) Proc. STAGS 98 LNCS , vol.1373 , pp. 39-49
    • Bradfield, J.C.1
  • 10
    • 0033293866 scopus 로고    scopus 로고
    • Fixpoints in arithmetic, transition systems and trees
    • Bradfield J.C. Fixpoints in arithmetic, transition systems and trees. Theoretical Informatics and Applications 33 4/5 (1999) 341-356
    • (1999) Theoretical Informatics and Applications , vol.33 , Issue.4-5 , pp. 341-356
    • Bradfield, J.C.1
  • 11
    • 0027113412 scopus 로고
    • Local model checking for infinite state spaces
    • Bradfield J.C., and P Stirling C. Local model checking for infinite state spaces. Theoret. Comput. Sci. 96 (1992) 57-174
    • (1992) Theoret. Comput. Sci. , vol.96 , pp. 57-174
    • Bradfield, J.C.1    P Stirling, C.2
  • 12
    • 0002921593 scopus 로고
    • On a decision method in restricted second order arithmetic
    • Proc. 1960 congress, Stanford Univ. Press, Stanford, CA
    • Proc. 1960 congress. Biichi J.R. On a decision method in restricted second order arithmetic. Logic, Methodology and Philosophy of Science (1962), Stanford Univ. Press, Stanford, CA 1-11
    • (1962) Logic, Methodology and Philosophy of Science , pp. 1-11
    • Biichi, J.R.1
  • 13
    • 85037030721 scopus 로고
    • Design and synthesis of synchronization skeletons using branching time temporal logic
    • Clarke E.M., and Emerson E.A. Design and synthesis of synchronization skeletons using branching time temporal logic. LNCS 131 (1981) 52-71
    • (1981) LNCS , Issue.131 , pp. 52-71
    • Clarke, E.M.1    Emerson, E.A.2
  • 14
  • 15
    • 0034404579 scopus 로고    scopus 로고
    • Logical questions concerning the μ-calculus: interpolation, Lyndon and Los-Tarski
    • d'Agostino G., and Hollenberg M. Logical questions concerning the μ-calculus: interpolation, Lyndon and Los-Tarski. J. Symbolic Logic 65 1 (2000) 310-332
    • (2000) J. Symbolic Logic , vol.65 , Issue.1 , pp. 310-332
    • d'Agostino, G.1    Hollenberg, M.2
  • 16
    • 0028420232 scopus 로고
    • CTL* and ECTL* as fragments of the modal mu-calculus
    • Dam M. CTL* and ECTL* as fragments of the modal mu-calculus. Theoret. Comput. Sci. 126 (1994) 77-96
    • (1994) Theoret. Comput. Sci. , vol.126 , pp. 77-96
    • Dam, M.1
  • 19
    • 0001449325 scopus 로고
    • Temporal and modal logic
    • van Leeuwen J. (Ed), Elsevier p]995-1072
    • Emerson E.A. Temporal and modal logic. In: van Leeuwen J. (Ed). Handbook of Theoretical Computer Science Volume B. (1990), Elsevier p]995-1072
    • (1990) Handbook of Theoretical Computer Science , vol.B
    • Emerson, E.A.1
  • 20
    • 84949208566 scopus 로고
    • Characterizing correctness properties of parallel programs using fixpoints
    • Emerson E.A., and Clarke E.M. Characterizing correctness properties of parallel programs using fixpoints. Procs ICALP '80 LNCS 85 (1980) 169-181
    • (1980) Procs ICALP '80 LNCS , vol.85 , pp. 169-181
    • Emerson, E.A.1    Clarke, E.M.2
  • 21
    • 0024141507 scopus 로고
    • The complexity of tree automata and logics of programs
    • Emerson E.A., and Jutla C.S. The complexity of tree automata and logics of programs. Proc. 29th IEEE FOCS (1988) 328-337
    • (1988) Proc. 29th IEEE FOCS , pp. 328-337
    • Emerson, E.A.1    Jutla, C.S.2
  • 22
    • 0026368952 scopus 로고
    • Tree automata, mu-calculus and determinacy
    • Emerson E.A., and Jutla C.S. Tree automata, mu-calculus and determinacy. Proc. 32nd IEEE FOCS (1991) 368-377
    • (1991) Proc. 32nd IEEE FOCS , pp. 368-377
    • Emerson, E.A.1    Jutla, C.S.2
  • 23
    • 0022956502 scopus 로고
    • Efficient model checking in fragments of the propositional mu-calculus
    • Emerson E.A., and Lei C.-L. Efficient model checking in fragments of the propositional mu-calculus. Proc. 1st IEEE LICS (1986) 267-278
    • (1986) Proc. 1st IEEE LICS , pp. 267-278
    • Emerson, E.A.1    Lei, C.-L.2
  • 25
    • 0002780749 scopus 로고
    • Assigning meanings to programs
    • Schwartz J.T. (Ed), American Mathematical Society, Providence
    • Floyd R. Assigning meanings to programs. In: Schwartz J.T. (Ed). Mathematical Aspects of Computer Science (1967), American Mathematical Society, Providence 19-32
    • (1967) Mathematical Aspects of Computer Science , pp. 19-32
    • Floyd, R.1
  • 26
    • 0039064922 scopus 로고    scopus 로고
    • On the restraining power of guards
    • Grädel E. On the restraining power of guards. J. Symbol. Logic 64 (1999) 1719-1742
    • (1999) J. Symbol. Logic , vol.64 , pp. 1719-1742
    • Grädel, E.1
  • 27
    • 40949140527 scopus 로고    scopus 로고
    • Grädel E., Thomas W., and Wilke T. (Eds)
    • In: Grädel E., Thomas W., and Wilke T. (Eds). Automata, Logics, and Infinite Games, LNCS (2002) 2500
    • (2002) Automata, Logics, and Infinite Games, LNCS , pp. 2500
  • 30
    • 85034843372 scopus 로고
    • On observing nondeterminism and concurrency
    • Hennessy M., and Milner R. On observing nondeterminism and concurrency. Procs ICALP '80 LNCS 85 (1980) 295-309
    • (1980) Procs ICALP '80 LNCS , vol.85 , pp. 295-309
    • Hennessy, M.1    Milner, R.2
  • 31
    • 84947903049 scopus 로고
    • Automata for the μ-calculus and related results
    • Janin D., and Walukiewicz I. Automata for the μ-calculus and related results. Proc. MFCS '95 LNCS 969 (1995) 552-562
    • (1995) Proc. MFCS '95 LNCS , Issue.969 , pp. 552-562
    • Janin, D.1    Walukiewicz, I.2
  • 32
    • 84948963145 scopus 로고    scopus 로고
    • On the expressive completeness of the propositional mu-calculus with respect to monadic second order logic
    • Janin D., and Walukiewicz I. On the expressive completeness of the propositional mu-calculus with respect to monadic second order logic. Proc. CONCUR '96 LNCS 1119 (1996) 263-277
    • (1996) Proc. CONCUR '96 LNCS , vol.1119 , pp. 263-277
    • Janin, D.1    Walukiewicz, I.2
  • 33
    • 0005542363 scopus 로고    scopus 로고
    • Using Automata to Characterise Fixpoint Temporal Logics
    • University of Edinburgh
    • Kaivola R. Using Automata to Characterise Fixpoint Temporal Logics. Ph.D. thesis (1997), University of Edinburgh
    • (1997) Ph.D. thesis
    • Kaivola, R.1
  • 34
    • 49049126479 scopus 로고
    • Results on the propositional mu-calculus
    • Kozen D. Results on the propositional mu-calculus. Theoret. Comput. Sci. 27 (1983) 333-354
    • (1983) Theoret. Comput. Sci. , vol.27 , pp. 333-354
    • Kozen, D.1
  • 35
    • 0040859656 scopus 로고
    • A finite model theorem for the propositional μ-calculus
    • Kozen D. A finite model theorem for the propositional μ-calculus. Studia Logica 47 (1988) 233-241
    • (1988) Studia Logica , vol.47 , pp. 233-241
    • Kozen, D.1
  • 36
    • 0001697777 scopus 로고
    • An elementary proof of the completeness of PDL
    • Kozen D., and Parikh R. An elementary proof of the completeness of PDL. Theoret. Comput. Sci. 14 (1981) 113-118
    • (1981) Theoret. Comput. Sci. , vol.14 , pp. 113-118
    • Kozen, D.1    Parikh, R.2
  • 37
    • 85034599450 scopus 로고
    • A decision procedure for the propositional μ-calculus
    • Kozen D., and Parikh R. A decision procedure for the propositional μ-calculus. LNCS 164 (1984) 313-325
    • (1984) LNCS , Issue.164 , pp. 313-325
    • Kozen, D.1    Parikh, R.2
  • 38
    • 15344345416 scopus 로고    scopus 로고
    • Expressive equivalence of least and inflationary fixed-point logic
    • Kreutzer S. Expressive equivalence of least and inflationary fixed-point logic. Annals of Pure and Applied Logic 130 1-3 (2004) 61-78
    • (2004) Annals of Pure and Applied Logic , vol.130 , Issue.1-3 , pp. 61-78
    • Kreutzer, S.1
  • 39
    • 0001667648 scopus 로고    scopus 로고
    • An automata-theoretic approach to branching-time model checking
    • Kupferman O., Vardi M., and Wolper P. An automata-theoretic approach to branching-time model checking. J. ACM 42 2 (2000) 312-360
    • (2000) J. ACM , vol.42 , Issue.2 , pp. 312-360
    • Kupferman, O.1    Vardi, M.2    Wolper, P.3
  • 40
    • 40949105966 scopus 로고    scopus 로고
    • Deciding the first level of the μ-calculus alternation hierarchy
    • LNCS
    • LNCS. Küsters R., and Wilke T. Deciding the first level of the μ-calculus alternation hierarchy. Proc. FSTTCS 2002 2556 (2002) 241-252
    • (2002) Proc. FSTTCS 2002 , Issue.2556 , pp. 241-252
    • Küsters, R.1    Wilke, T.2
  • 41
    • 0017472779 scopus 로고
    • Proving the correctness of multiprocess programs
    • Lamport L. Proving the correctness of multiprocess programs. IEEE Trans. Software Eng. 2 (1977) 125-143
    • (1977) IEEE Trans. Software Eng. , vol.2 , pp. 125-143
    • Lamport, L.1
  • 42
    • 84947755850 scopus 로고    scopus 로고
    • A hierarchy theorem for the mu-calculus
    • Lenzi G. A hierarchy theorem for the mu-calculus. Proc. ICALP '96 LNCS 1099 (1996) 87-109
    • (1996) Proc. ICALP '96 LNCS , vol.1099 , pp. 87-109
    • Lenzi, G.1
  • 43
    • 84947904189 scopus 로고    scopus 로고
    • Fully local and efficient evaluation of alternating fixed points
    • Liu X., Ramakrishnan C.R., and Smolka S.A. Fully local and efficient evaluation of alternating fixed points. Proc. TACAS '98 LNCS 1384 (1998) 5-19
    • (1998) Proc. TACAS '98 LNCS , vol.1384 , pp. 5-19
    • Liu, X.1    Ramakrishnan, C.R.2    Smolka, S.A.3
  • 45
    • 0003464918 scopus 로고    scopus 로고
    • Verification of Modal Properties Using Boolean Equation Systems
    • Technical University of Munich
    • Mader A. Verification of Modal Properties Using Boolean Equation Systems. PhD Thesis (1997), Technical University of Munich
    • (1997) PhD Thesis
    • Mader, A.1
  • 46
    • 0040139823 scopus 로고
    • Absence of interpolation and of Beth's property in temporal logics with 'the next' operation
    • Maksimova L. Absence of interpolation and of Beth's property in temporal logics with 'the next' operation. Siberian Mathematical Journal 32 6 (1991) 109-113
    • (1991) Siberian Mathematical Journal , vol.32 , Issue.6 , pp. 109-113
    • Maksimova, L.1
  • 47
    • 0014615661 scopus 로고
    • Formalization of properties of recursively defined functions
    • Manna Z., and Pnueli A. Formalization of properties of recursively defined functions. Proc. ACM STOC (1969) 201-210
    • (1969) Proc. ACM STOC , pp. 201-210
    • Manna, Z.1    Pnueli, A.2
  • 48
    • 0020920624 scopus 로고
    • How to cook a temporal proof system for your pet language
    • Manna Z., and Pnueli A. How to cook a temporal proof system for your pet language. Proc. 10th ACM POPL (1983) 141-154
    • (1983) Proc. 10th ACM POPL , pp. 141-154
    • Manna, Z.1    Pnueli, A.2
  • 51
    • 84913355219 scopus 로고
    • Regular expressions for infinite trees and a standard form of automata
    • LNCS
    • LNCS. Mostowski A.W. Regular expressions for infinite trees and a standard form of automata. Computa- tion Theory 208 (1984) 157-168
    • (1984) Computa- tion Theory , vol.208 , pp. 157-168
    • Mostowski, A.W.1
  • 52
    • 85026897255 scopus 로고
    • On fixed point clones
    • Niwinski D. On fixed point clones. Proc. ICALP '86 LNCS 226 (1986) 464-473
    • (1986) Proc. ICALP '86 LNCS , vol.226 , pp. 464-473
    • Niwinski, D.1
  • 53
    • 0004017533 scopus 로고    scopus 로고
    • Bisimulation-invariant Ptime and higher-dimensional mu-calculus
    • Otto M. Bisimulation-invariant Ptime and higher-dimensional mu-calculus. Theoret. Comput. Sci. 224 (1999) 237-266
    • (1999) Theoret. Comput. Sci. , vol.224 , pp. 237-266
    • Otto, M.1
  • 54
    • 84957069698 scopus 로고    scopus 로고
    • Eliminating recursion in the mu-calculus
    • Otto M. Eliminating recursion in the mu-calculus. Proc. STACS '99, LNCS 1563 (1999) 531-540
    • (1999) Proc. STACS '99, LNCS , vol.1563 , pp. 531-540
    • Otto, M.1
  • 55
    • 0014651649 scopus 로고
    • Fixpoint induction and proofs of program properties
    • Edin- burgh University Press
    • D P. Fixpoint induction and proofs of program properties. Machine Intelligence 5 (1969), Edin- burgh University Press 59-78
    • (1969) Machine Intelligence , vol.5 , pp. 59-78
  • 56
    • 85034789348 scopus 로고
    • Semantical considerations of Floyd-Hoare logic
    • Pratt V. Semantical considerations of Floyd-Hoare logic. Proc. 16th IEEE FOCS (1976) 109-121
    • (1976) Proc. 16th IEEE FOCS , pp. 109-121
    • Pratt, V.1
  • 57
    • 0001594044 scopus 로고
    • A near-optimal method for reasoning about action
    • Pratt V. A near-optimal method for reasoning about action. Journal of Comput. and System Sciences 20 (1980) 231-254
    • (1980) Journal of Comput. and System Sciences , vol.20 , pp. 231-254
    • Pratt, V.1
  • 58
    • 0002197709 scopus 로고
    • A decidable mu-calculus
    • Pratt V. A decidable mu-calculus. Proc. 22nd IEEE FOCS (1982) 421-427
    • (1982) Proc. 22nd IEEE FOCS , pp. 421-427
    • Pratt, V.1
  • 59
    • 84968501436 scopus 로고
    • Decidability of second-order theories and automata on infinite trees
    • Rabin M.O. Decidability of second-order theories and automata on infinite trees. Transactions of American Mathematical Society 141 (1969) 1-35
    • (1969) Transactions of American Mathematical Society , vol.141 , pp. 1-35
    • Rabin, M.O.1
  • 60
    • 84947781453 scopus 로고
    • Local model checking games
    • Stirling C. Local model checking games. Proc. Concur '95 LNCS 962 (1995) 1-11
    • (1995) Proc. Concur '95 LNCS , vol.962 , pp. 1-11
    • Stirling, C.1
  • 62
    • 0001132880 scopus 로고
    • Local model checking in the modal mu-calculus
    • Stirling C., and Walker D. Local model checking in the modal mu-calculus. Theor. Comput. Sci. 89 (1991) 161-177
    • (1991) Theor. Comput. Sci. , vol.89 , pp. 161-177
    • Stirling, C.1    Walker, D.2
  • 63
    • 0024681890 scopus 로고
    • An automata theoretic decision procedure for the propositional mu-calculus
    • Streett R.S., and Emerson E.A. An automata theoretic decision procedure for the propositional mu-calculus. Information and Computation 81 (1989) 249-264
    • (1989) Information and Computation , vol.81 , pp. 249-264
    • Streett, R.S.1    Emerson, E.A.2
  • 64
    • 23744483720 scopus 로고
    • Propositional dynamic logic of looping and converse
    • Streett R. Propositional dynamic logic of looping and converse. Proc. 13th ACM STOC (1981) 375-383
    • (1981) Proc. 13th ACM STOC , pp. 375-383
    • Streett, R.1
  • 65
    • 0001568609 scopus 로고    scopus 로고
    • Languages, Automata, and Logic
    • Rozen- berg G., and Salomaa A. (Eds), Springer-Verlag, New York
    • Thomas W. Languages, Automata, and Logic. In: Rozen- berg G., and Salomaa A. (Eds). Handbook of Formal Language Theory Vol. III (1998), Springer-Verlag, New York 389-455
    • (1998) Handbook of Formal Language Theory , vol.III , pp. 389-455
    • Thomas, W.1
  • 66
    • 85011693404 scopus 로고
    • A temporal fixpoint calculus
    • Vardi M.Y. A temporal fixpoint calculus. Proc. 15th POPL (1988) 250-259
    • (1988) Proc. 15th POPL , pp. 250-259
    • Vardi, M.Y.1
  • 67
    • 0001652558 scopus 로고    scopus 로고
    • Why is modal logic so robustly decidable?
    • Immerman N., and Kolaitis Ph. (Eds), American Mathematical Society
    • Vardi M.Y. Why is modal logic so robustly decidable?. In: Immerman N., and Kolaitis Ph. (Eds). Descriptive Complexity and Finite Models (1997), American Mathematical Society
    • (1997) Descriptive Complexity and Finite Models
    • Vardi, M.Y.1
  • 68
    • 84878592842 scopus 로고    scopus 로고
    • Reasoning about the past with two-way automata
    • Vardi M.Y. Reasoning about the past with two-way automata. Proc. ICALP '98 LNCS 1443 (1998) 628-641
    • (1998) Proc. ICALP '98 LNCS , vol.1443 , pp. 628-641
    • Vardi, M.Y.1
  • 70
    • 0034711982 scopus 로고    scopus 로고
    • Completeness of Kozen's axiomatisation of the propositional μ-calculus
    • Walukiewicz I. Completeness of Kozen's axiomatisation of the propositional μ-calculus. Information and Computation 157 (2000) 142-182
    • (2000) Information and Computation , vol.157 , pp. 142-182
    • Walukiewicz, I.1


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