An Automata-Theoretic Approach to Linear Temporal Logic

The automata-theoretic approach to linear temporal logic uses the theory of automata as a unifying paradigm for program specification, verification, and synthesis. Both programs and specifications are in essence descriptions of computations. These computations can be viewed as words over some alphabet. Thus, programs and specifications can be viewed as descriptions of languages over some alphabet. The automata-theoretic perspective considers the relationships between programs and their specifications as relationships between languages. By translating programs and specifications to automata, questions about programs and their specifications can be reduced to questions about automata. More specifically, questions such as satisfiability of specifications and correctness of programs with respect to their specifications can be reduced to questions such as nonemptiness and containment of automata.

[1]  Harry Rudin.  Network Protocols and Tools to Help Produce Them , 1987 .

[2]  David E. Muller,et al.  Weak alternating automata give a simple explanation of why most temporal and dynamic logics are decidable in exponential time , 1988, [1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science.

[3]  E. A Emerson,et al.  Using Branching Time Logic to Synthesize Synchronization Skeletons , 1982 .

[4]  Leslie Lamport,et al.  Proving Liveness Properties of Concurrent Programs , 1982, TOPL.

[5]  Robert P. Kurshan,et al.  Computer-Aided Verification of Coordinating Processes: The Automata-Theoretic Approach , 2014 .

[6]  E. Allen Emerson,et al.  On simultaneously determinizing and complementing omega -automata , 1989, [1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science.

[7]  Joseph Y. Halpern,et al.  “Sometimes” and “not never” revisited: on branching versus linear time temporal logic , 1986, JACM.

[8]  Neil D. Jones,et al.  Space-Bounded Reducibility among Combinatorial Problems , 1975, J. Comput. Syst. Sci..

[9]  Morton Davis,et al.  7. Infinite Games of Perfect Information , 1964 .

[10]  Journal of the Association for Computing Machinery , 1961, Nature.

[11]  Saharon Shelah,et al.  On the temporal analysis of fairness , 1980, POPL '80.

[12]  Fred Kröger,et al.  Temporal Logic of Programs , 1987, EATCS Monographs on Theoretical Computer Science.

[13]  Edmund M. Clarke,et al.  Using Branching Time Temporal Logic to Synthesize Synchronization Skeletons , 1982, Sci. Comput. Program..

[14]  Robert McNaughton,et al.  Testing and Generating Infinite Sequences by a Finite Automaton , 1966, Inf. Control..

[15]  Yaacov Choueka,et al.  Theories of Automata on omega-Tapes: A Simplified Approach , 1974, J. Comput. Syst. Sci..

[16]  Charles Rackoff,et al.  The Emptiness Problem for Automata on Infinite Trees , 1972, SWAT.

[17]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[18]  Martín Abadi,et al.  Realizable and Unrealizable Specifications of Reactive Systems , 1989, ICALP.

[19]  Pierre Wolper,et al.  An Automata-Theoretic Approach to Automatic Program Verification (Preliminary Report) , 1986, LICS.

[20]  Pierre Wolper,et al.  Memory-efficient algorithms for the verification of temporal properties , 1990, Formal Methods Syst. Des..

[21]  S. Sieber.  On a decision method in restricted second-order arithmetic , 1960 .

[22]  Leslie Lamport,et al.  "Sometime" is sometimes "not never": on the temporal logic of programs , 1980, POPL '80.

[23]  Pierre Wolper,et al.  The Complementation Problem for Büchi Automata with Appplications to Temporal Logic , 1987, Theor. Comput. Sci..

[24]  E. Muller David,et al.  Alternating automata on infinite trees , 1987 .

[25]  Ernst L. Leiss,et al.  Succint Representation of Regular Languages by Boolean Automata , 1981, Theor. Comput. Sci..

[26]  Dana S. Scott,et al.  Finite Automata and Their Decision Problems , 1959, IBM J. Res. Dev..

[27]  Zohar Manna,et al.  The Temporal Logic of Reactive and Concurrent Systems , 1991, Springer New York.

[28]  Wolfgang Thomas,et al.  Automata on Infinite Objects , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[29]  Albert R. Meyer,et al.  The Equivalence Problem for Regular Expressions with Squaring Requires Exponential Space , 1972, SWAT.

[30]  Ernst L. Leiss,et al.  On Equations for Regular Languages, Finite Automata, and Sequential Networks , 1980, Theor. Comput. Sci..

[31]  David L. Dill,et al.  Trace theory for automatic hierarchical verification of speed-independent circuits , 1989, ACM distinguished dissertations.

[32]  S. Safra,et al.  On the complexity of omega -automata , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[33]  Pierre Wolper,et al.  Reasoning About Infinite Computations , 1994, Inf. Comput..

[34]  Chin-Laung Lei,et al.  Modalities for Model Checking: Branching Time Logic Strikes Back , 1987, Sci. Comput. Program..

[35]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[36]  Walter J. Savitch,et al.  Relationships Between Nondeterministic and Deterministic Tape Complexities , 1970, J. Comput. Syst. Sci..

[37]  Satoru Miyano,et al.  Alternating Finite Automata on omega-Words , 1984, CAAP.

[38]  Ming T. Liu.  Protocol Engineering , 1989, Adv. Comput..

[39]  Amir Pnueli,et al.  The Glory of the Past , 1985, Logic of Programs.

[40]  A. R. Meyer,et al.  Economy of Description by Automata, Grammars, and Formal Systems , 1971, SWAT.

[41]  M. Rabin.  Automata on Infinite Objects and Church's Problem , 1972 .

[42]  Amir Pnueli,et al.  On the synthesis of a reactive module , 1989, POPL '89.

[43]  J. R. Büchi,et al.  Solving sequential conditions by finite-state strategies , 1969 .

[44]  E. A Emerson,et al.  Model Checking Under Generalized Fairness Constraints , 1984 .

[45]  E. Allen Emerson,et al.  The complexity of tree automata and logics of programs , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[46]  Chin-Laung Lei,et al.  Modalities for model checking (extended abstract): branching time strikes back , 1985, POPL.

[47]  Amir Pnueli,et al.  Checking that finite state concurrent programs satisfy their linear specification , 1985, POPL.

[48]  Pierre Wolper,et al.  Reasoning about infinite computation paths , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[49]  E. Allen Emerson,et al.  Automata, Tableaux and Temporal Logics (Extended Abstract) , 1985, Logic of Programs.

[50]  A. Prasad Sistla,et al.  The complexity of propositional linear temporal logics , 1982, STOC '82.

[51]  M. Rabin.  Decidability of second-order theories and automata on infinite trees , 1968 .

[52]  Pierre Wolper,et al.  Synthesis of Communicating Processes from Temporal Logic Specifications , 1981, TOPL.

[53]  Amir Pnueli,et al.  Is the interesting part of process logic uninteresting?: a translation from PL to PDL , 1982, POPL '82.

[54]  Moshe Y. Vardi.  Nontraditional Applications of Automata Theory , 1994, TACS.

[55]  David E. Muller,et al.  Alternating Automata on Infinite Trees , 1987, Theor. Comput. Sci..

[56]  Larry J. Stockmeyer,et al.  Improved upper and lower bounds for modal logics of programs , 1985, STOC '85.

[57]  Amir Pnueli,et al.  On the Development of Reactive Systems , 1989, Logics and Models of Concurrent Systems.