Related papers: Parikh's Theorem Made Symbolic
Threshold automata are a formalism for modeling and analyzing fault-tolerant distributed algorithms, recently introduced by Konnov, Veith, and Widder, describing protocols executed by a fixed but arbitrary number of processes. We conduct…
The $\textbf{P}$ vs. $\textbf{NP}$ problem is an important problem in contemporary mathematics and theoretical computer science. Many proofs have been proposed to this problem. This paper proposes a theoretic proof for $\textbf{P}$ vs.…
A \emph{data automaton} is a finite automaton equipped with variables (counters or registers) ranging over infinite data domains. A trace of a data automaton is an alternating sequence of alphabet symbols and values taken by the counters…
Resolving complex information needs that come with multiple constraints should consider enforcing the logical operators encoded in the query (i.e., conjunction, disjunction, negation) on the candidate answer set. Current retrieval systems…
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…
Several abstract machines that operate on symbolic input alphabets have been proposed in the last decade, for example, symbolic automata or lattice automata. Applications of these types of automata include software security analysis and…
The classical pattern matching paradigm is that of seeking occurrences of one string - the pattern, in another - the text, where both strings are drawn from an alphabet set $\Sigma$. Assuming the text length is $n$ and the pattern length is…
Solving parity games, which are equivalent to modal $\mu$-calculus model checking, is a central algorithmic problem in formal methods. Besides the standard computation model with the explicit representation of games, another important…
Automata learning has many applications in artificial intelligence and software engineering. Central to these applications is the $L^*$ algorithm, introduced by Angluin. The $L^*$ algorithm learns deterministic finite-state automata (DFAs)…
Generating effective test inputs for a software system requires that these inputs be valid, as they will otherwise be rejected without reaching actual functionality. In the absence of a specification for the input language, common test…
This paper investigates the possibility of performing automated reasoning in probabilistic logic when probabilities are expressed by means of linguistic quantifiers. Each linguistic term is expressed as a prescribed interval of proportions.…
Numerous computer systems use dynamic control and data structures of unbounded size. These data structures have often the character of trees or they can be encoded as trees with some additional pointers. This is exploited by some currently…
Minimizing the size of finite automata is a fundamental problem in theoretical computer science. Beyond standard minimization, further reductions can be achieved by decomposing an automaton into smaller components whose languages combine…
Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…
Here we define a new unification algorithm for terms interpreted in semantic domains denoted by a subclass of regular types here called deterministic regular types. This reflects our intention not to handle the semantic universe as a…
We present a new approach for solving string equations as extensions of Nielsen transformations. Key to our work are the combination of three techniques: a power operator for strings; generalisations of Parikh images; and equality…
Computer-aided analysis of security protocols heavily relies on equational theories to model cryptographic primitives. Most automated verifiers for security protocols focus on equational theories that satisfy the Finite Variant Property…
We investigate a subclass of languages recognized by vector addition systems, namely languages of nondeterministic Parikh automata. While the regularity problem (is the language of a given automaton regular?) is undecidable for this model,…
A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…
This paper presents a new solution to the containment problem for extended regular expressions that extends basic regular expressions with intersection and complement operators and consider regular expressions on infinite alphabets based on…