“Sometimes” and “not never” revisited: on branching versus linear time temporal logic
Journal of the ACM (JACM) - The MIT Press scientific computation series
Automatic verification of finite-state concurrent systems using temporal logic specifications
ACM Transactions on Programming Languages and Systems (TOPLAS)
Theoretical Computer Science
Automata-Theoretic techniques for modal logics of programs
Journal of Computer and System Sciences
Alternating automata, the weak monadic theory of the tree, and its complexity
International Colloquium on Automata, Languages and Programming on Automata, languages and programming
Improved upper and lower bounds for modal logics of programs
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Alternating automata on infinite trees
Theoretical Computer Science
Proceedings on Temporal logic in specification
Proceedings on Temporal logic in specification
On-line model checking for finite linear temporal logic specifications
Proceedings of the international workshop on Automatic verification methods for finite state systems
Handbook of theoretical computer science (vol. B)
Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Local model checking in the modal mu-calculus
TAPSOFT '89 2nd international joint conference on Theory and practice of software development
Model checking and Boolean graphs
ESOP'92 Symposium proceedings on 4th European symposium on programming
Memory-efficient algorithms for the verification of temporal properties
Formal Methods in System Design - Special issue on computer-aided verification: general methods
A linear-time model-checking algorithm for the alternation-free modal mu-calculus
Formal Methods in System Design - Special issue on computer-aided verification: special methods II
Reasoning about infinite computations
Information and Computation
Limits to parallel computation: P-completeness theory
Limits to parallel computation: P-completeness theory
Automated temporal reasoning about reactive systems
Proceedings of the VIII Banff Higher order workshop conference on Logics for concurrency : structure versus automata: structure versus automata
Weak alternating automata and tree automata emptiness
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Checking that finite state concurrent programs satisfy their linear specification
POPL '85 Proceedings of the 12th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Computational problems related to the design of normal form relational schemas
ACM Transactions on Database Systems (TODS)
On the menbership problem for functional and multivalued dependencies in relational databases
ACM Transactions on Database Systems (TODS)
Log Space Recognition and Translation of Parenthesis Languages
Journal of the ACM (JACM)
Journal of the ACM (JACM)
"Sometime" is sometimes "not never": on the temporal logic of programs
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The Propositional Mu-Calculus is Elementary
Proceedings of the 11th Colloquium on Automata, Languages and Programming
TACAs '96 Proceedings of the Second International Workshop on Tools and Algorithms for Construction and Analysis of Systems
Efficent Local Model-Checking for Fragments of teh Modal µ-Calculus
TACAs '96 Proceedings of the Second International Workshop on Tools and Algorithms for Construction and Analysis of Systems
Branching Time Temporal Logic and Amorphous Tree Automata
CONCUR '93 Proceedings of the 4th International Conference on Concurrency Theory
A Linear Local Model Checking Algorithm for CTL
CONCUR '93 Proceedings of the 4th International Conference on Concurrency Theory
On the Complexity of Branching Modular Model Checking (Extended Abstract)
CONCUR '95 Proceedings of the 6th International Conference on Concurrency Theory
A Space-Efficient On-the-fly Algorithm for Real-Time Model Checking
CONCUR '96 Proceedings of the 7th International Conference on Concurrency Theory
On the Relation of Programs and Computations to Models of Temporal Logic
Temporal Logic in Specification
Specification and verification of concurrent systems in CESAR
Proceedings of the 5th Colloquium on International Symposium on Programming
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
Efficient Local Correctness Checking
CAV '92 Proceedings of the Fourth International Workshop on Computer Aided Verification
On Model-Checking for Fragments of µ-Calculus
CAV '93 Proceedings of the 5th International Conference on Computer Aided Verification
On the Random Walk Method for Protocol Testing
CAV '94 Proceedings of the 6th International Conference on Computer Aided Verification
Efficient Checking of Behavioural Relations and Modal Assertions using Fixed-Point Inversion
Proceedings of the 7th International Conference on Computer Aided Verification
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
Yet Another Process Logic (Preliminary Version)
Proceedings of the Carnegie Mellon Workshop on Logic of Programs
Automata, Tableaux and Temporal Logics (Extended Abstract)
Proceedings of the Conference on Logic of Programs
Verification Tools for Finite-State Concurrent Systems
A Decade of Concurrency, Reflections and Perspectives, REX School/Symposium
On the complexity of modular model checking
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
Efficient model checking via the equational /spl mu/-calculus
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Partial-Order Methods for Model Checking: From Linear Time to Branching Time
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Freedom, Weakness, and Determinism: From Linear-Time to Branching-Time
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Alternating-time Temporal Logic
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
An automata-theoretic approach to modular model checking
ACM Transactions on Programming Languages and Systems (TOPLAS)
Weak alternating automata are not that weak
ACM Transactions on Computational Logic (TOCL)
The regular viewpoint on PA-processes
Theoretical Computer Science
Information and Computation
On the complexity of verifying concurrent transition systems
Information and Computation
Model Checking of Safety Properties
Formal Methods in System Design
Alternating-time temporal logic
Journal of the ACM (JACM)
Model exploration with temporal logic query checking
Proceedings of the 10th ACM SIGSOFT symposium on Foundations of software engineering
Complexity of weak acceptance conditions in tree automata
Information Processing Letters
Model exploration with temporal logic query checking
ACM SIGSOFT Software Engineering Notes
Deciding LTL over Mazurkiewicz traces
Data & Knowledge Engineering - Special issue: Temporal representation and reasoning
Model Checking Games for the Alternation-Free µ-Calculus and Alternating Automata
LPAR '99 Proceedings of the 6th International Conference on Logic Programming and Automated Reasoning
Games and Model Checking for Guarded Logics
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
LPAR '02 Proceedings of the 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
Local Parallel Model Checking for the Alternation-Free µ-Calculus
Proceedings of the 9th International SPIN Workshop on Model Checking of Software
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
Parallel Model Checking for the Alternation Free µ-Calculus
TACAS 2001 Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Coverage Metrics for Temporal Logic Model Checking
TACAS 2001 Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
A Parametric Analysis of the State Explosion Problem in Model Checking
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
The State Explosion Problem from Trace to Bisimulation Equivalence
FOSSACS '00 Proceedings of the Third International Conference on Foundations of Software Science and Computation Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software,ETAPS 2000
The Complexity of Model Checking Mobile Ambients
FoSSaCS '01 Proceedings of the 4th International Conference on Foundations of Software Science and Computation Structures
State Space Reductions for Alternating Büchi Automata
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Efficient Model Checking Via Büchi Tableau Automata
CAV '01 Proceedings of the 13th International Conference on Computer Aided Verification
A Practical Approach to Coverage in Model Checking
CAV '01 Proceedings of the 13th International Conference on Computer Aided Verification
Model Checking Linear Properties of Prefix-Recognizable Systems
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Automatic Abstraction Using Generalized Model Checking
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
On the Variable Hierarchy of the Modal µ-Calculus
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
On the Use of Weak Automata for Deciding Linear Arithmetic with Integer and Real Variables
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
On the expressivity and complexity of quantitative branching-time temporal logics
Theoretical Computer Science - Latin American theoretical informatics
PCK50 Proceedings of the Paris C. Kanellakis memorial workshop on Principles of computing & knowledge: Paris C. Kanellakis memorial workshop on the occasion of his 50th birthday
Partial-Order Methods for Model Checking: From Linear Time to Branching Time
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
On temporal logic versus datalog
Theoretical Computer Science - Logic and complexity in computer science
Temporalized logics and automata for time granularity
Theory and Practice of Logic Programming
PSPACE-completeness of Modular Supervisory Control Problems
Discrete Event Dynamic Systems
Specification and verification of data-driven web services
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
From linear time to branching time
ACM Transactions on Computational Logic (TOCL)
An effective decision procedure for linear arithmetic over the integers and reals
ACM Transactions on Computational Logic (TOCL)
An axiomatization of bisimulation quantifiers via the µ-calculus
Theoretical Computer Science
Simulation relations for alternating Büchi automata
Theoretical Computer Science
A decidable class of problems for control under partial observation
Information Processing Letters
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
On the universal and existential fragments of the μ-calculus
Theoretical Computer Science - Tools and algorithms for the construction and analysis of systems (TACAS 2003)
Complete axiomatization and decidability of alternating-time temporal logic
Theoretical Computer Science
Efficient timed model checking for discrete-time systems
Theoretical Computer Science
A parametric analysis of the state-explosion problem in model checking
Journal of Computer and System Sciences
Probabilistic temporal logics via the modal mu-calculus
Theoretical Computer Science
On the complexity of practical ATL model checking
AAMAS '06 Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems
The complexity of model checking concurrent programs against CTLK specifications
AAMAS '06 Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems
Coverage metrics for temporal logic model checking
Formal Methods in System Design
Automata-Theoretic Decision Procedures for Information Logics
Fundamenta Informaticae
Specification and verification of data-driven Web applications
Journal of Computer and System Sciences
Expressing and Verifying Temporal and Structural Properties of Mobile Agents
Fundamenta Informaticae - SPECIAL ISSUE ON CONCURRENCY SPECIFICATION AND PROGRAMMING (CS&P 2005) Ruciane-Nide, Poland, 28-30 September 2005
Generalising automaticity to modal properties of finite structures
Theoretical Computer Science
Complexity results on branching-time pushdown model checking
Theoretical Computer Science
GSTE is partitioned model checking
Formal Methods in System Design
Groebner bases computation in Boolean rings for symbolic model checking
MOAS'07 Proceedings of the 18th conference on Proceedings of the 18th IASTED International Conference: modelling and simulation
A game-based framework for CTL counterexamples and 3-valued abstraction-refinement
ACM Transactions on Computational Logic (TOCL)
Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems
What causes a system to satisfy a specification?
ACM Transactions on Computational Logic (TOCL)
Some succinctness properties of Ω-DTAFA
SEPADS'06 Proceedings of the 5th WSEAS International Conference on Software Engineering, Parallel and Distributed Systems
Model Checking and Preprocessing
AI*IA '07 Proceedings of the 10th Congress of the Italian Association for Artificial Intelligence on AI*IA 2007: Artificial Intelligence and Human-Oriented Computing
Model Checking: From Tools to Theory
25 Years of Model Checking
ATL* Satisfiability Is 2EXPTIME-Complete
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Run-Time Monitoring of Electronic Contracts
ATVA '08 Proceedings of the 6th International Symposium on Automated Technology for Verification and Analysis
Model Checking Quantitative Linear Time Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
Program Complexity in Hierarchical Module Checking
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
LTL Generalized Model Checking Revisited
VMCAI '09 Proceedings of the 10th International Conference on Verification, Model Checking, and Abstract Interpretation
An Automata-Theoretic Dynamic Completeness Criterion for Bounded Model-Checking
VMCAI '09 Proceedings of the 10th International Conference on Verification, Model Checking, and Abstract Interpretation
An Automata-based Approach for CTL*; With Constraints
Electronic Notes in Theoretical Computer Science (ENTCS)
Temporal Logic Patterns for Querying Qualitative Models of Genetic Regulatory Networks
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
Explaining Counterexamples Using Causality
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
MCMAS: A Model Checker for the Verification of Multi-Agent Systems
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Easy Yet Hard: Model Checking Strategies of Agents
Computational Logic in Multi-Agent Systems
An Automata-Theoretic Approach to Regular XPath
DBPL '09 Proceedings of the 12th International Symposium on Database Programming Languages
The planning spectrum: one, two, three, infinity
Journal of Artificial Intelligence Research
Groebner bases computation in Boolean rings for symbolic model checking
MS '07 The 18th IASTED International Conference on Modelling and Simulation
A Tableau System for the Modal μ-Calculus
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
FM '09 Proceedings of the 2nd World Congress on Formal Methods
Language-Emptiness Checking of Alternating Tree Automata Using Symbolic Reachability Analysis
Electronic Notes in Theoretical Computer Science (ENTCS)
A decidable class of problems for control under partial observation
Information Processing Letters
Logic and automata: a match made in heaven
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Oracle circuits for branching-time model checking
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
Model checking on trees with path equivalences
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
On the universal and existential fragments of the µ-calculus
TACAS'03 Proceedings of the 9th international conference on Tools and algorithms for the construction and analysis of systems
The ComBack method: extending hash compaction with backtracking
ICATPN'07 Proceedings of the 28th international conference on Applications and theory of Petri nets and other models of concurrency
Formal Methods in System Design
A generic constructive solution for concurrent games with expressive constraints on strategies
ATVA'07 Proceedings of the 5th international conference on Automated technology for verification and analysis
Enriched µ-calculus pushdown module checking
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
The complexity of temporal logic with until and since over ordinals
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
The complexity of CTL* + linear past
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Coalgebraic logic and synthesis of mealy machines
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Model checking freeze LTL over one-counter automata
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
EXPTIME tableaux for the coalgebraic µ-calculus
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Linear game automata: decidable hierarchy problems for stripped-down alternating tree automata
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
On the complexity of branching-time logics
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
The Complexity of Epistemic Model Checking: Clock Semantics and Branching Time
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
On the (Un-)Decidability of Model Checking Resource-Bounded Agents
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
An automata-theoretic approach to infinite-state systems
Time for verification
Alternation removal in büchi automata
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Graded computation tree logic with binary coding
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Relentful strategic reasoning in alternating-time temporal logic
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
The modal µ-calculus caught off guard
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
Temporal property verification as a program analysis task
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Software model checking using languages of nested trees
ACM Transactions on Programming Languages and Systems (TOPLAS)
Max and sum semantics for alternating weighted automata
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
Improved model checking of hierarchical systems
Information and Computation
The complexity of enriched µ-calculi
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Multi-valued model checking games
ATVA'05 Proceedings of the Third international conference on Automated Technology for Verification and Analysis
Treewidth in verification: local vs. global
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Reasoning about Co-Büchi tree automata
ICTAC'04 Proceedings of the First international conference on Theoretical Aspects of Computing
Multi-valued model checking games
Journal of Computer and System Sciences
Satisfiability and finite model property for the alternating-time µ-calculus
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
Improved model checking of hierarchical systems
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
Deciding full branching time logic by program transformation
LOPSTR'09 Proceedings of the 19th international conference on Logic-Based Program Synthesis and Transformation
Model checking for database theoreticians
ICDT'05 Proceedings of the 10th international conference on Database Theory
Weak automata for the linear time µ-calculus
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Bounded model checking for weak alternating büchi automata
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
The variable hierarchy of the µ-calculus is strict
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Complexity results on branching-time pushdown model checking
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Explaining counterexamples using causality
Formal Methods in System Design
Journal of Computer and System Sciences
Finding shortest witnesses to the nonemptiness of automata on infinite words
CONCUR'06 Proceedings of the 17th international conference on Concurrency Theory
State space representation for verification of open systems
AMAST'06 Proceedings of the 11th international conference on Algebraic Methodology and Software Technology
The complexity of model checking concurrent programs against CTLK specifications
DALT'06 Proceedings of the 4th international conference on Declarative Agent Languages and Technologies
Model checking information flow in reactive systems
VMCAI'12 Proceedings of the 13th international conference on Verification, Model Checking, and Abstract Interpretation
SBMC: symmetric bounded model checking
VECoS'10 Proceedings of the Fourth international conference on Verification and Evaluation of Computer and Communication Systems
ACM Transactions on Computational Logic (TOCL)
Survey: Linear Temporal Logic Symbolic Model Checking
Computer Science Review
Temporal property verification as a program analysis task
Formal Methods in System Design
p-Automata: New foundations for discrete-time probabilistic verification
Performance Evaluation
Specification and verification of multi-agent systems
ESSLLI'10 Proceedings of the 2010 conference on ESSLLI 2010, and ESSLLI 2011 conference on Lectures on Logic and Computation
Model Checking Temporal-Epistemic Logic Using Alternating Tree Automata
Fundamenta Informaticae - Concurrency Specification and Programming (CS&P)
Expressing and Verifying Temporal and Structural Properties of Mobile Agents
Fundamenta Informaticae - SPECIAL ISSUE ON CONCURRENCY SPECIFICATION AND PROGRAMMING (CS&P 2005) Ruciane-Nide, Poland, 28-30 September 2005
Automata-Theoretic Decision Procedures for Information Logics
Fundamenta Informaticae
Communicative commitments: Model checking and complexity analysis
Knowledge-Based Systems
Quantified CTL: expressiveness and model checking
CONCUR'12 Proceedings of the 23rd international conference on Concurrency Theory
What makes ATL* decidable? a decidable fragment of strategy logic
CONCUR'12 Proceedings of the 23rd international conference on Concurrency Theory
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
Pushdown module checking with imperfect information
Information and Computation
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Model Checking Higher-Order Programs
Journal of the ACM (JACM)
Reasoning about nondeterminism in programs
Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation
From model checking to model measuring
CONCUR'13 Proceedings of the 24th international conference on Concurrency Theory
Quantitative reactive modeling and verification
Computer Science - Research and Development
Synthesis of hierarchical systems
Science of Computer Programming
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
On the Boundary of Behavioral Strategies
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
A Translation of the Existential Model Checking Problem from MITL to HLTL
Fundamenta Informaticae
| Hi-index | 0.01 |
Translating linear temporal logic formulas to automata has proven to be an effective approach for implementing linear-time model-checking, and for obtaining many extensions and improvements to this verification method. On the other hand, for branching temporal logic, automata-theoretic techniques have long been thought to introduce an exponential penalty, making them essentially useless for model-checking. Recently, Bernholtz and Grumberg [1993] have shown that this exponential penalty can be avoided, though they did not match the linear complexity of non-automata-theoretic algorithms. In this paper, we show that alternating tree automata are the key to a comprehensive automata-theoretic framework for branching temporal logics. Not only can they be used to obtain optimal decision procedures, as was shown by Muller et al., but, as we show here, they also make it possible to derive optimal model-checking algorithms. Moreover, the simple combinatorial structure that emerges from the automata-theoretic approach opens up new possibilities for the implementation of branching-time model checking and has enabled us to derive improved space complexity bounds for this long-standing problem.