Graph Logics with Rational Relations

Barceló, Pablo; Figueira, Diego; Libkin, Leonid

doi:10.2168/lmcs-9(3:1)2013

Cited by 22 publications

(52 citation statements)

References 32 publications

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“…The (binary) relation recognized by a transducer T is denoted by [T ] ⊆ Σ * × Σ * . Synchronous transducers are known to recognize the set of regular relations, also called synchronized rational relations in the literature (see [8,6,3]). In the following, the size of a transducer T , written |T |, will denote the size of its transition relation: |T | = |∆|.…”

Section: Del-generated Models and Regular Structuresmentioning

confidence: 99%

Automata Techniques for Epistemic Protocol Synthesis

Maubert

Pinchinat²

2014

Electron. Proc. Theor. Comput. Sci.

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In this work we aim at applying automata techniques to problems studied in Dynamic Epistemic Logic, such as epistemic planning. To do so, we first remark that repeatedly executing ad infinitum a propositional event model from an initial epistemic model yields a relational structure that can be finitely represented with automata. This correspondence, together with recent results on uniform strategies, allows us to give an alternative decidability proof of the epistemic planning problem for propositional events, with as by-products accurate upper-bounds on its time complexity, and the possibility to synthesize a finite word automaton that describes the set of all solution plans. In fact, using automata techniques enables us to solve a much more general problem, that we introduce and call epistemic protocol synthesis.

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Section: Del-generated Models and Regular Structuresmentioning

confidence: 99%

Automata Techniques for Epistemic Protocol Synthesis

Maubert

Pinchinat²

2014

Electron. Proc. Theor. Comput. Sci.

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“…When exploring larger complexities, the hierarchy includes non primitive-recursive classes, for which quite a few complete problems have arisen in the recent years, e.g. F ω in [35,28,47,44,19,10,33], F ω ω in [13,39,32,6,12,7], F ω ω ω in [27], and F ε 0 in [26].…”

Section: Fast Growing Complexity Classesmentioning

confidence: 99%

The Power of Well-Structured Systems

Schmitz

Schnoebelen

2013

Lecture Notes in Computer Science

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Abstract. Well-structured systems, aka WSTSs, are computational models where the set of possible configurations is equipped with a wellquasi-ordering which is compatible with the transition relation between configurations. This structure supports generic decidability results that are important in verification and several other fields.This paper recalls the basic theory underlying well-structured systems and shows how two classic decision algorithms can be formulated as an exhaustive search for some "bad" sequences. This lets us describe new powerful techniques for the complexity analysis of WSTS algorithms. Recently, these techniques have been successful in precisely characterising the power, in a complexity-theoretical sense, of several important WSTS models like unreliable channel systems, monotonic counter machines, or networks of timed systems.

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“…Fortunately, recent years have seen the possibility of recovering some decidability of string constraint languages with multiple string operations, while retaining applicability for constraints that arise in practical symbolic execution applications. This is done by imposing syntactic restrictions including acyclicity [6,3], solved form [28], and straight-line [42,30,18]. These restrictions are known to be satisfied by many existing string constraint benchmarks, e.g., Kaluza [50], Stranger [59], SLOG [57,30], and mutation XSS benchmarks of [42].…”

Section: Introductionmentioning

confidence: 99%

Decision procedures for path feasibility of string-manipulating programs with complex operations

Chen

Hague

Lin

et al. 2019

Proc. ACM Program. Lang.

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The design and implementation of decision procedures for checking path feasibility in string-manipulating programs is an important problem, with such applications as symbolic execution of programs with strings and automated detection of cross-site scripting (XSS) vulnerabilities in web applications. A (symbolic) path is given as a finite sequence of assignments and assertions (i.e. without loops), and checking its feasibility amounts to determining the existence of inputs that yield a successful execution. Modern programming languages (e.g. JavaScript, PHP, and Python) support many complex string operations, and strings are also often implicitly modified during a computation in some intricate fashion (e.g. by some autoescaping mechanisms).In this paper we provide two general semantic conditions which together ensure the decidability of path feasibility: (1) each assertion admits regular monadic decomposition (i.e. is an effectively recognisable relation), and (2) each assignment uses a (possibly nondeterministic) function whose inverse relation preserves regularity. We show that the semantic conditions are expressive since they are satisfied by a multitude of string operations including concatenation, one-way and two-way finite-state transducers, replaceAll functions (where the replacement string could contain variables), string-reverse functions, regularexpression matching, and some (restricted) forms of letter-counting/length functions. The semantic conditions also strictly subsume existing decidable string theories (e.g. straightline fragments, and acyclic logics), and most existing benchmarks (e.g. most of Kaluza's, and all of SLOG's, Stranger's, and SLOTH's benchmarks). Our semantic conditions also yield a conceptually simple decision procedure, as well as an extensible architecture of a string solver in that a user may easily incorporate his/her own string functions into the solver by simply providing code for the pre-image computation without worrying about other parts of the solver. Despite these, the semantic conditions are unfortunately too general to provide a fast and complete decision procedure. We provide strong theoretical evidence for this in the form of complexity results. To rectify this problem, we propose two solutions. Our main solution is to allow only partial string functions (i.e., prohibit nondeterminism) in condition (2). This restriction is satisfied in many cases in practice, and yields decision procedures that are effective in both theory and practice. Whenever nondeterministic functions are still needed (e.g. the string function split), our second solution is to provide a syntactic fragment that provides a support of nondeterministic functions, and operations like one-way transducers, replaceAll (with constant replacement string), the string-reverse function, concatenation, and regular-expression matching. We show that this fragment can be reduced to an existing solver SLOTH that exploits fast model checking algorithms like IC3.We provide an efficient implementation of our decision p...

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Graph Logics with Rational Relations

Abstract: 2012 ACM CCS: [Theory of computation]: Formal languages and automata theory; Theory and algorithms for application domains-Database theory-Database query languages (principles); Design and analysis of algorithms.

Cited by 22 publications

References 32 publications

Automata Techniques for Epistemic Protocol Synthesis

Automata Techniques for Epistemic Protocol Synthesis

The Power of Well-Structured Systems

Decision procedures for path feasibility of string-manipulating programs with complex operations

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