Results 1  10
of
21
MONA Implementation Secrets
, 2000
"... The MONA tool provides an implementation of the decision procedures for the logics WS1S and WS2S. It has been used for numerous applications, and it is remarkably efficient in practice, even though it faces a theoretically nonelementary worstcase complexity. The implementation has matured over a p ..."
Abstract

Cited by 83 (6 self)
 Add to MetaCart
(Show Context)
The MONA tool provides an implementation of the decision procedures for the logics WS1S and WS2S. It has been used for numerous applications, and it is remarkably efficient in practice, even though it faces a theoretically nonelementary worstcase complexity. The implementation has matured over a period of six years. Compared to the first naive version, the present tool is faster by several orders of magnitude. This speedup is obtained from many different contributions working on all levels of the compilation and execution of formulas. We present a selection of implementation "secrets" that have been discovered and tested over the years, including formula reductions, DAGification, guided tree automata, threevalued logic, eager minimization, BDDbased automata representations, and cacheconscious data structures. We describe these techniques and quantify their respective effects by experimenting with separate versions of the MONA tool that in turn omit each of them.
Hybrid Logics
"... This chapter provides a modern overview of the field of hybrid logic. Hybrid logics are extensions of standard modal logics, involving symbols that name individual states in models. The first results that are nowadays considered as part of the field date back to the early work of Arthur ..."
Abstract

Cited by 62 (18 self)
 Add to MetaCart
This chapter provides a modern overview of the field of hybrid logic. Hybrid logics are extensions of standard modal logics, involving symbols that name individual states in models. The first results that are nowadays considered as part of the field date back to the early work of Arthur
The Complexity of Propositional Linear Temporal Logics in Simple Cases
 Information and Computation
, 1998
"... this paper we investigate this issue and consider model checking and satisfiability for all fragments of PLTL obtainable by restricting (1) the temporal connectives allowed, (2) the number of atomic propositions, and (3) the temporal height. Key Words: logic in computer science, computational comple ..."
Abstract

Cited by 61 (1 self)
 Add to MetaCart
this paper we investigate this issue and consider model checking and satisfiability for all fragments of PLTL obtainable by restricting (1) the temporal connectives allowed, (2) the number of atomic propositions, and (3) the temporal height. Key Words: logic in computer science, computational complexity, verification, temporal logic, model checking 1.
Bounded Model Construction for Monadic SecondOrder Logics
 In 12th International Conference on ComputerAided Verification (CAV’00), number 1855 in LNCS
, 2000
"... The monadic logics M2LStr and WS1S have been successfully used for verification, although they are nonelementary decidable. Motivated by ideas from bounded model checking, we investigate procedures for bounded model construction for these logics. The problem is, given a formula and a bound k, does ..."
Abstract

Cited by 36 (2 self)
 Add to MetaCart
The monadic logics M2LStr and WS1S have been successfully used for verification, although they are nonelementary decidable. Motivated by ideas from bounded model checking, we investigate procedures for bounded model construction for these logics. The problem is, given a formula and a bound k, does there exist a word model for of length k. We give a bounded model construction algorithm for M2LStr that runs in a time exponential in k. For WS1S, we prove a negative result: bounded model construction is as hard as validity checking, i.e., it is nonelementary. From this, negative results for other monadic logics, such as S1S, follow. We present too preliminary tests using a SATbased implementation of bounded model construction; for certain problem classes it can find counterexamples substantially faster than automatabased decision procedures.
Combining WS1S and HOL
 Frontiers of Combining Systems 2, volume 7 of Studies in Logic and Computation
, 1998
"... We investigate the combination of the weak secondorder monadic logic of one successor (WS1S) with higherorder logic (HOL). We show how these two logics can be combined, how theorem provers based on them can be safely integrated, and how the result can be used. In particular, we present an embeddin ..."
Abstract

Cited by 26 (4 self)
 Add to MetaCart
We investigate the combination of the weak secondorder monadic logic of one successor (WS1S) with higherorder logic (HOL). We show how these two logics can be combined, how theorem provers based on them can be safely integrated, and how the result can be used. In particular, we present an embedding of the semantics of WS1S in HOL that provides a basis for coupling the MONA system, a decision procedure for WS1S, with an implementation of HOL in the Isabelle system. Afterwards, we describe methods that reduce problems formalized in HOL to problems in the language of WS1S. We present applications to arithmetic reasoning and proving properties of parameterized sequential systems.
Structural and Behavioral Modeling with Monadic Logics
 IN THE TWENTYNINTH IEEE INTERNATIONAL SYMPOSIUM ON MULTIPLEVALUED LOGIC. IEEE COMPUTER SOCIETY
, 1999
"... Logic offers the possibility of modeling and reasoning about hardware and software. But which logic? We propose monadic logics of strings and trees as good candidates for many kinds of discrete systems. These logics are natural, decidable, yet substantially more expressive, extensions of Boolean log ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
Logic offers the possibility of modeling and reasoning about hardware and software. But which logic? We propose monadic logics of strings and trees as good candidates for many kinds of discrete systems. These logics are natural, decidable, yet substantially more expressive, extensions of Boolean logic. We motivate their applicability through examples.
Decision Procedures for Inductive Boolean Functions based on Alternating Automata
 In 12th International Conference on ComputerAided Veri CAV'00, volume 1855 of LNCS
, 2000
"... We show how alternating automata provide decision procedures for the equality of inductively defined Boolean functions and present applications to reasoning about parameterized families of circuits. We use alternating word automata to formalize families of linearly structured circuits and alternatin ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
We show how alternating automata provide decision procedures for the equality of inductively defined Boolean functions and present applications to reasoning about parameterized families of circuits. We use alternating word automata to formalize families of linearly structured circuits and alternating tree automata to formalize families of tree structured circuits. We provide complexity bounds for deciding the equality of function (or circuit) families and show how our decision procedures can be implemented using BDDs. In comparison to previous work, our approach is simpler, has better complexity bounds, and, in the case of tree structured families, is more general.
Extracting Exact Time Bounds From Logical Proofs
 LOPSTR 2001, volume 2372 of LNCS
, 2002
"... Accurate evaluation of delays of combinatorial circuits is crucial in circuit verification and design. In this paper we present a logical approach to timing analysis which allows us to compute exact stabilization bounds while proving the correctness of the boolean behavior. ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
Accurate evaluation of delays of combinatorial circuits is crucial in circuit verification and design. In this paper we present a logical approach to timing analysis which allows us to compute exact stabilization bounds while proving the correctness of the boolean behavior.
Combining Logic Programs and Monadic Second Order Logics by Program Transformation
"... We present a program synthesis method based on unfold/fold transformation rules which can be used for deriving terminating definite logic programs from formulas of the Weak Monadic Second Order theory of one successor (WS1S). This synthesis method can also be used as a proof method which is a decisi ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
We present a program synthesis method based on unfold/fold transformation rules which can be used for deriving terminating definite logic programs from formulas of the Weak Monadic Second Order theory of one successor (WS1S). This synthesis method can also be used as a proof method which is a decision procedure for closed formulas of WS1S.